title: Battle of Dunkirk

text: A considerable number of British troops remained in France after Dunkirk to the south of the River Somme. These numbered some 140,000 men, mostly logistic support and lines-of-communications troops, but also including the 51st (Highland) Division and the remnants of the 1st Armoured Division. On 2 June, Lieutenant General Brooke was ordered back to France to form a Second BEF together with two further infantry divisions to follow, a project which Brooke believed was doomed to failure. After learning that most of the 51st Division had surrendered, having been cut off at St Valery-en-Caux on the Channel coast, Brooke spoke to Churchill by telephone on 14 June and persuaded him to allow the evacuation of all the remaining British forces in France. In Operation Aerial, 144,171 British, 18,246 French, 24,352 Polish and 1,939 Czech troops were embarked in ships at several major ports along the west coast of France and returned to England, along with much of their equipment. The only major mishap was the sinking of the with the loss of perhaps 6,000 men. The last British troops left France on 25 June, the day the French Armistice came into force.


title: Battle of Dunkirk

text: British press later exploited the successful evacuation of Dunkirk in 1940, and particularly the role of the "Dunkirk little ships", very effectively. Many of them were private vessels such as fishing boats and pleasure cruisers, but commercial vessels such as ferries also contributed to the force, including a number from as far away as the Isle of Man and Glasgow. These smaller vessels—guided by naval craft across the Channel from the Thames Estuary and from Dover—assisted in the official evacuation. Being able to move closer into the beachfront shallows than larger craft, the "little ships" acted as shuttles to and from the larger ships, lifting troops who were queuing in the water, many waiting shoulder-deep in water for hours. The term "Dunkirk Spirit" refers to the solidarity of the British people in times of adversity.


title: Battle of Dunkirk

text: A commemorative medal was established in 1960 by the French National Association of Veterans of the Fortified Sector of Flanders and Dunkirk on behalf of the town of Dunkirk. The medal was initially awarded only to the French defenders of Dunkirk, but in 1970 the qualification was expanded to include British forces who served in the Dunkirk sector and their rescue forces, including the civilians who volunteered to man the "little ships".


title: Battle of Dunkirk

text: The design of the bronze medal included the arms of the town of Dunkirk on one side, and ""Dunkerque 1940"" on the reverse side.


title: Investment banking

text: Investment banking pertains to certain activities of a financial services company or a corporate division that consist in advisory-based financial transactions on behalf of individuals, corporations, and governments. Traditionally associated with corporate finance, such a bank might assist in raising financial capital by underwriting or acting as the client's agent in the issuance of debt or equity securities. An investment bank may also assist companies involved in mergers and acquisitions (M&A) and provide ancillary services such as market making, trading of derivatives and equity securities, FICC services (fixed income instruments, currencies, and commodities) or research (macroeconomic, credit or equity research). Most investment banks maintain prime brokerage and asset management departments in conjunction with their investment research businesses. As an industry, it is broken up into the Bulge Bracket (upper tier), Middle Market (mid-level businesses), and boutique market (specialized businesses).


title: Investment banking

text: Unlike commercial banks and retail banks, investment banks do not take deposits. From the passage of Glass–Steagall Act in 1933 until its repeal in 1999 by the Gramm–Leach–Bliley Act, the United States maintained a separation between investment banking and commercial banks. Other industrialized countries, including G7 countries, have historically not maintained such a separation. As part of the Dodd–Frank Wall Street Reform and Consumer Protection Act of 2010 ("Dodd–Frank Act of 2010"), the Volcker Rule asserts some institutional separation of investment banking services from commercial banking.


title: Investment banking

text: All investment banking activity is classed as either "sell side" or "buy side". The "sell side" involves trading securities for cash or for other securities (e.g. facilitating transactions, market-making), or the promotion of securities (e.g. underwriting, research, etc.). The "buy side" involves the provision of advice to institutions that buy investment services. Private equity funds, mutual funds, life insurance companies, unit trusts, and hedge funds are the most common types of buy-side entities.


title: Investment banking

text: An investment bank can also be split into private and public functions with a screen separating the two to prevent information from crossing. The private areas of the bank deal with private insider information that may not be publicly disclosed, while the public areas, such as stock analysis, deal with public information. An advisor who provides investment banking services in the United States must be a licensed broker-dealer and subject to U.S. Securities and Exchange Commission (SEC) and Financial Industry Regulatory Authority (FINRA) regulation.


title: Investment banking

text: The Dutch East India Company was the first company to issue bonds and shares of stock to the general public. It was also the first publicly traded company, being the first company to be listed on an official stock exchange.


title: Investment banking

text: Investment banking has changed over the years, beginning as a partnership firm focused on underwriting security issuance, i.e. initial public offerings (IPOs) and secondary market offerings, brokerage, and mergers and acquisitions, and evolving into a "full-service" range including securities research, proprietary trading, and investment management. In the 21st century, the SEC filings of the major independent investment banks such as Goldman Sachs and Morgan Stanley reflect three product segments:


title: Investment banking

text: In the United States, commercial banking and investment banking were separated by the Glass–Steagall Act, which was repealed in 1999. The repeal led to more "universal banks" offering an even greater range of services. Many large commercial banks have therefore developed investment banking divisions through acquisitions and hiring. Notable large banks with significant investment banks include JPMorgan Chase, Bank of America, Citigroup, Credit Suisse, Deutsche Bank, UBS, and Barclays.


title: Investment banking

text: After the financial crisis of 2007–08 and the subsequent passage of the "Dodd-Frank Act of 2010", regulations have limited certain investment banking operations, notably with the Volcker Rule's restrictions on proprietary trading.


title: Investment banking

text: The traditional service of underwriting security issues has declined as a percentage of revenue. As far back as 1960, 70% of Merrill Lynch's revenue was derived from transaction commissions while "traditional investment banking" services accounted for 5%. However, Merrill Lynch was a relatively "retail-focused" firm with a large brokerage network.


title: Investment banking

text: Investment banking is split into front office, middle office, and back office activities. While large service investment banks offer all lines of business, both "sell side" and "buy side", smaller sell-side investment firms such as boutique investment banks and small broker-dealers focus on investment banking and sales/trading/research, respectively.


title: Investment banking

text: Investment banks offer services to both corporations issuing securities and investors buying securities. For corporations, investment bankers offer information on when and how to place their securities on the open market, an activity very important to an investment bank's reputation. Therefore, investment bankers play a very important role in issuing new security offerings.


title: Investment banking

text: "Front office" is generally described as a revenue-generating role. There are two main areas within front office: investment banking and markets.


title: Investment banking

text: Corporate finance is the aspect of investment banks which involves helping customers raise funds in capital markets and giving advice on mergers and acquisitions (M&A);


title: Investment banking

text: This work may involve, i.a., subscribing investors to a security issuance, coordinating with bidders, or negotiating with a merger target.


title: Investment banking

text: A pitch book of financial information is generated to market the bank to a potential M&A client; if the pitch is successful, the bank arranges the deal for the client.


title: Investment banking

text: The investment banking division (IBD) is generally divided into industry coverage and product coverage groups.


title: Investment banking

text: Industry coverage groups focus on a specific industry—such as healthcare, public finance (governments), FIG (financial institutions group), industrials, TMT (technology, media, and telecommunications), P&E (power & energy), consumer/retail, food & beverage, corporate defense and governance—and maintain relationships with corporations within the industry to bring in business for the bank.


title: Investment banking

text: Product coverage groups focus on financial products—such as mergers and acquisitions, leveraged finance, public finance, asset finance and leasing, structured finance, restructuring, equity, and debt issuance.


title: Investment banking

text: Recent legal and regulatory developments in the U.S. will likely alter the makeup of the group of arrangers and financiers willing to arrange and provide financing for certain highly leveraged transactions.


title: Investment banking

text: On behalf of the bank and its clients, a large investment bank's primary function is buying and selling products.


title: Investment banking

text: "Sales" is the term for the investment bank's sales force, whose primary job is to call on institutional and high-net-worth investors to suggest trading ideas (on a caveat emptor basis) and take orders. Sales desks then communicate their clients' orders to the appropriate trading rooms, which can price and execute trades, or structure new products that fit a specific need.


title: Investment banking

text: Sales make deals tailored to their corporate customers' needs, that is, their terms are often specific. Focusing on their customer relationship, they may deal on the whole range of asset types.


title: Investment banking

text: (In distinction, trades negotiated by market-makers usually bear standard terms; in market making, traders will buy and sell financial products with the goal of making money on each trade.


title: Investment banking

text: "Structuring" has been a relatively recent activity as derivatives have come into play, with highly technical and numerate employees working on creating complex structured products which typically offer much greater margins and returns than underlying cash securities, so-called "yield enhancement". In 2010, investment banks came under pressure as a result of selling complex derivatives contracts to local municipalities in Europe and the US.


title: Investment banking

text: "Strategists" advise external as well as internal clients on the strategies that can be adopted in various markets. Ranging from derivatives to specific industries, strategists place companies and industries in a quantitative framework with full consideration of the macroeconomic scene. This strategy often affects the way the firm will operate in the market, the direction it would like to take in terms of its proprietary and flow positions, the suggestions salespersons give to clients, as well as the way structurers create new products.


title: Investment banking

text: Banks also undertake risk through proprietary trading, performed by a special set of traders who do not interface with clients and through "principal risk"—risk undertaken by a trader after he buys or sells a product to a client and does not hedge his total exposure.


title: Investment banking

text: Here, and in general, banks seek to maximize profitability for a given amount of risk on their balance sheet.


title: Investment banking

text: Note here that the FRTB framework has underscored the distinction between the "Trading book" and the "Banking book"


title: Investment banking

text: The necessity for numerical ability in sales and trading has created jobs for physics, computer science, mathematics, and engineering PhDs who act as "front office" quantitative analysts.


title: Investment banking

text: The securities research division reviews companies and writes reports about their prospects, often with "buy", "hold", or "sell" ratings. Investment banks typically have sell-side analysts which cover various industries. Their sponsored funds or proprietary trading offices will also have buy-side research.


title: Investment banking

text: Research also covers credit risk, fixed income, macroeconomics, and quantitative analysis, all of which are used internally and externally to advise clients; alongside "Equity", these may be separate "groups".


title: Investment banking

text: While the research division may or may not generate revenue (based on policies at different banks), its resources are used to assist traders in trading, the sales force in suggesting ideas to customers, and investment bankers by covering their clients. Research also serves outside clients with investment advice (such as institutional investors and high-net-worth individuals) in the hopes that these clients will execute suggested trade ideas through the sales and trading division of the bank, and thereby generate revenue for the firm.


title: Investment banking

text: With MiFID II requiring sell-side research teams in banks to charge for research, the business model for research is increasingly becoming revenue-generating. External rankings of researchers are becoming increasingly important, and banks have started the process of monetizing research publications, client interaction times, meetings with clients etc.


title: Investment banking

text: There is a potential conflict of interest between the investment bank and its analysis, in that published analysis can impact the performance of a security (in the secondary markets or an initial public offering) or influence the relationship between the banker and its corporate clients, and vice versa regarding material non-public information (MNPI), thereby affecting the bank's profitability.


title: Investment banking

text: This area of the bank includes treasury management, internal controls (such as Risk), and internal corporate strategy.


title: Investment banking

text: Corporate treasury is responsible for an investment bank's funding, capital structure management, and liquidity risk monitoring; it is (co)responsible for the bank's funds transfer pricing (FTP) framework.


title: Investment banking

text: Internal control tracks and analyzes the capital flows of the firm, the finance division is the principal adviser to senior management on essential areas such as controlling the firm's global risk exposure and the profitability and structure of the firm's various businesses via dedicated trading desk product control teams. In the United States and United Kingdom, a comptroller (or financial controller) is a senior position, often reporting to the chief financial officer.


title: Investment banking

text: Risk management involves analyzing the market and credit risk that an investment bank or its clients take onto their balance sheet during transactions or trades.


title: Investment banking

text: Middle office "Credit Risk" focuses around capital markets activities, such as syndicated loans, bond issuance, restructuring, and leveraged finance.


title: Investment banking

text: These are not considered "front office" as they tend not to be client-facing and rather 'control' banking functions from taking too much risk.


title: Investment banking

text: "Market Risk" is the control function for the Markets' business and conducts review of sales and trading activities utilizing the VaR model.


title: Investment banking

text: Other Middle office "Risk Groups" include country risk, operational risk, and counterparty risks which may or may not exist on a bank to bank basis.


title: Investment banking

text: Front office risk teams, on the other hand, engage in revenue-generating activities involving debt structuring, restructuring, syndicated loans, and securitization for clients such as corporates, governments, and hedge funds.


title: Investment banking

text: Here "Credit Risk Solutions", are a key part of capital market transactions, involving debt structuring, exit financing, loan amendment, project finance, leveraged buy-outs, and sometimes portfolio hedging.


title: Investment banking

text: The "Market Risk Team" provides services to investors via derivative solutions, portfolio management, portfolio consulting, and risk advisory.


title: Investment banking

text: J.P. Morgan IB Risk works with investment banking to execute transactions and advise investors, although its Finance & Operation risk groups focus on middle office functions involving internal, non-revenue generating, operational risk controls. The credit default swap, for instance, is a famous credit risk hedging solution for clients invented by J.P. Morgan's Blythe Masters during the 1990s.


title: Investment banking

text: The Loan Risk Solutions group within Barclays' investment banking division and Risk Management and Financing group housed in Goldman Sach's securities division are client-driven franchises.


title: Investment banking

text: Note, however, that risk management groups such as credit risk, operational risk, internal risk control, and legal risk are restrained to internal business functions — including firm balance-sheet risk analysis and assigning the trading cap — that are independent of client needs, even though these groups may be responsible for deal approval that directly affects capital market activities.


title: Investment banking

text: Similarly, the "Internal corporate strategy" group, tackling firm management and profit strategy, unlike corporate strategy groups that advise clients, is non-revenue regenerating yet a key functional role within investment banks.


title: Investment banking

text: This list is not a comprehensive summary of all middle-office functions within an investment bank, as specific desks within front and back offices may participate in internal functions.


title: Investment banking

text: The back office data-checks trades that have been conducted, ensuring that they are not wrong, and transacts the required transfers. Many banks have outsourced operations. It is, however, a critical part of the bank.


title: Investment banking

text: Every major investment bank has considerable amounts of in-house software, created by the technology team, who are also responsible for technical support. Technology has changed considerably in the last few years as more sales and trading desks are using electronic trading. Some trades are initiated by complex algorithms for hedging purposes.


title: Investment banking

text: Firms are responsible for compliance with local and foreign government regulations and internal regulations.


title: Investment banking

text: As an industry, it is broken up into the Bulge Bracket (upper tier), Middle Market (mid-level businesses), and boutique market (specialized businesses). There are various trade associations throughout the world which represent the industry in lobbying, facilitate industry standards, and publish statistics. The International Council of Securities Associations (ICSA) is a global group of trade associations.


title: Investment banking

text: In the United States, the Securities Industry and Financial Markets Association (SIFMA) is likely the most significant; however, several of the large investment banks are members of the American Bankers Association Securities Association (ABASA), while small investment banks are members of the National Investment Banking Association (NIBA).


title: Investment banking

text: In Europe, the European Forum of Securities Associations was formed in 2007 by various European trade associations. Several European trade associations (principally the London Investment Banking Association and the European SIFMA affiliate) combined in November 2009 to form the Association for Financial Markets in Europe (AFME).


title: Investment banking

text: In the securities industry in China, the Securities Association of China is a self-regulatory organization whose members are largely investment banks.


title: Investment banking

text: Global investment banking revenue increased for the fifth year running in 2007, to a record US$84 billion, which was up 22% on the previous year and more than double the level in 2003. Subsequent to their exposure to United States sub-prime securities investments, many investment banks have experienced losses. As of late 2012, global revenues for investment banks were estimated at $240 billion, down about a third from 2009, as companies pursued less deals and traded less. Differences in total revenue are likely due to different ways of classifying investment banking revenue, such as subtracting proprietary trading revenue.


title: Investment banking

text: In terms of total revenue, SEC filings of the major independent investment banks in the United States show that investment banking (defined as M&A advisory services and security underwriting) made up only about 15–20% of total revenue for these banks from 1996 to 2006, with the majority of revenue (60+% in some years) brought in by "trading" which includes brokerage commissions and proprietary trading; the proprietary trading is estimated to provide a significant portion of this revenue.


title: Investment banking

text: The United States generated 46% of global revenue in 2009, down from 56% in 1999. Europe (with Middle East and Africa) generated about a third while Asian countries generated the remaining 21%. The industry is heavily concentrated in a small number of major financial centers, including New York City, City of London, Frankfurt, Hong Kong, Singapore, and Tokyo. The majority of the world's largest Bulge Bracket investment banks and their investment managers are headquartered in New York and are also important participants in other financial centers. The city of London has historically served as a hub of European M&A activity, often facilitating the most capital movement and corporate restructuring in the area. Meanwhile, Asian cities are receiving a growing share of M&A activity.


title: Investment banking

text: According to estimates published by the International Financial Services London, for the decade prior to the financial crisis in 2008, M&A was a primary source of investment banking revenue, often accounting for 40% of such revenue, but dropped during and after the financial crisis. Equity underwriting revenue ranged from 30% to 38%, and fixed-income underwriting accounted for the remaining revenue.


title: Investment banking

text: Revenues have been affected by the introduction of new products with higher margins; however, these innovations are often copied quickly by competing banks, pushing down trading margins. For example, brokerages commissions for bond and equity trading is a commodity business, but structuring and trading derivatives have higher margins because each over-the-counter contract has to be uniquely structured and could involve complex pay-off and risk profiles. One growth area is private investment in public equity (PIPEs, otherwise known as Regulation D or Regulation S). Such transactions are privately negotiated between companies and accredited investors.


title: Investment banking

text: Banks also earned revenue by securitizing debt, particularly mortgage debt prior to the financial crisis. Investment banks have become concerned that lenders are securitizing in-house, driving the investment banks to pursue vertical integration by becoming lenders, which is allowed in the United States since the repeal of the Glass–Steagall Act in 1999.


title: Investment banking

text: According to "The Wall Street Journal", in terms of total M&A advisory fees for the whole of 2020, the top ten investment banks were as listed in the table below. Many of these firms belong either to the Bulge Bracket (upper tier), Middle Market (mid-level businesses), or are elite boutique investment banks (independent investment banks).


title: Investment banking

text: The above list is just a ranking of the advisory arm (M&A advisory, syndicated loans, equity capital markets, and debt capital markets) of each bank and does not include the generally much larger portion of revenues from sales and trading and asset management. Mergers and acquisitions and capital markets are also often covered by "The Wall Street Journal" and Bloomberg.


title: Investment banking

text: The financial crisis of 2007–2008 led to the collapse of several notable investment banks, such as the bankruptcy of Lehman Brothers (one of the largest investment banks in the world) and the hurried sale of Merrill Lynch and the much smaller Bear Stearns to much larger banks, which effectively rescued them from bankruptcy. The entire financial services industry, including numerous investment banks, was bailed out by government taxpayer funded loans through the Troubled Asset Relief Program (TARP). Surviving U.S. investment banks such as Goldman Sachs and Morgan Stanley converted to traditional bank holding companies to accept TARP relief. Similar situations occurred across the globe with countries rescuing their banking industry. Initially, banks received part of a $700 billion TARP intended to stabilize the economy and thaw the frozen credit markets. Eventually, taxpayer assistance to banks reached nearly $13 trillion—most without much scrutiny— lending did not increase, and credit markets remained frozen.


title: Investment banking

text: The crisis led to questioning of the business model of the investment bank without the regulation imposed on it by Glass–Steagall. Once Robert Rubin, a former co-chairman of Goldman Sachs, became part of the Clinton administration and deregulated banks, the previous conservatism of underwriting established companies and seeking long-term gains was replaced by lower standards and short-term profit. Formerly, the guidelines said that in order to take a company public, it had to be in business for a minimum of five years and it had to show profitability for three consecutive years. After deregulation, those standards were gone, but small investors did not grasp the full impact of the change.


title: Investment banking

text: A number of former Goldman Sachs top executives, such as Henry Paulson and Ed Liddy, were in high-level positions in government and oversaw the controversial taxpayer-funded bank bailout. The TARP Oversight Report released by the Congressional Oversight Panel found that the bailout tended to encourage risky behavior and "corrupt[ed] the fundamental tenets of a market economy".


title: Investment banking

text: Under threat of a subpoena, Goldman Sachs revealed that it received $12.9 billion in taxpayer aid, $4.3 billion of which was then paid out to 32 entities, including many overseas banks, hedge funds, and pensions. The same year it received $10 billion in aid from the government, it also paid out multimillion-dollar bonuses; the total paid in bonuses was $4.82 billion. Similarly, Morgan Stanley received $10 billion in TARP funds and paid out $4.475 billion in bonuses.


title: Investment banking

text: The investment banking industry, and many individual investment banks, have come under criticism for a variety of reasons, including perceived conflicts of interest, overly large pay packages, cartel-like or oligopolistic behavior, taking both sides in transactions, and more. Investment banking has also been criticised for its opacity.


title: Investment banking

text: Conflicts of interest may arise between different parts of a bank, creating the potential for market manipulation, according to critics. Authorities that regulate investment banking, such as the Financial Conduct Authority (FCA) in the United Kingdom and the SEC in the United States, require that banks impose a "Chinese wall" to prevent communication between investment banking on one side and equity research and trading on the other. However, critics say such a barrier does not always exist in practice. Independent advisory firms that exclusively provide corporate finance advice argue that their advice is not conflicted, unlike bulge bracket banks.


title: Investment banking

text: Conflicts of interest often arise in relation to investment banks' equity research units, which have long been part of the industry. A common practice is for equity analysts to initiate coverage of a company in order to develop relationships that lead to highly profitable investment banking business. In the 1990s, many equity researchers allegedly traded positive stock ratings for investment banking business. Alternatively, companies may threaten to divert investment banking business to competitors unless their stock was rated favorably. Laws were passed to criminalize such acts, and increased pressure from regulators and a series of lawsuits, settlements, and prosecutions curbed this business to a large extent following the 2001 stock market tumble after the dot-com bubble.


title: Investment banking

text: Philip Augar, author of "The Greed Merchants", said in an interview that, "You cannot simultaneously serve the interest of issuer clients and investing clients. And it’s not just underwriting and sales; investment banks run proprietary trading operations that are also making a profit out of these securities."


title: Investment banking

text: Many investment banks also own retail brokerages. During the 1990s, some retail brokerages sold consumers securities which did not meet their stated risk profile. This behavior may have led to investment banking business or even sales of surplus shares during a public offering to keep public perception of the stock favorable.


title: Investment banking

text: Since investment banks engage heavily in trading for their own account, there is always the temptation for them to engage in some form of front running—the illegal practice whereby a broker executes orders for their own account before filling orders previously submitted by their customers, thereby benefiting from any changes in prices induced by those orders.


title: Investment banking

text: Documents under seal in a decade-long lawsuit concerning eToys.com's IPO but obtained by "New York Times"' Wall Street Business columnist Joe Nocera alleged that IPOs managed by Goldman Sachs and other investment bankers involved asking for kickbacks from their institutional clients who made large profits flipping IPOs which Goldman had intentionally undervalued. Depositions in the lawsuit alleged that clients willingly complied with these demands because they understood it was necessary in order to participate in future hot issues. "Reuters" Wall Street correspondent Felix Salmon retracted his earlier, more conciliatory statements on the subject and said he believed that the depositions show that companies going public and their initial consumer stockholders are both defrauded by this practice, which may be widespread throughout the IPO finance industry. The case is ongoing, and the allegations remain unproven.


title: Investment banking

text: Investment banking is often criticized for the enormous pay packages awarded to those who work in the industry. According to Bloomberg Wall Street's five biggest firms paid over $3 billion to their executives from 2003 to 2008, "while they presided over the packaging and sale of loans that helped bring down the investment-banking system".


title: Investment banking

text: The highly generous pay packages include $172 million for Merrill Lynch CEO Stanley O'Neal from 2003 to 2007, before it was bought by Bank of America in 2008, and $161 million for Bear Stearns' James Cayne before the bank collapsed and was sold to JPMorgan Chase in June 2008.


title: Investment banking

text: Such pay arrangements have attracted the ire of Democrats and Republicans in the United States Congress, who demanded limits on executive pay in 2008 when the U.S. government was bailing out the industry with a $700 billion financial rescue package.


title: Investment banking

text: Writing in the Global Association of Risk Professionals journal, Aaron Brown, a vice president at Morgan Stanley, says "By any standard of human fairness, of course, investment bankers make obscene amounts of money."


title: SMS

text: Short Message/Messaging Service, commonly abbreviated as SMS, is a text messaging service component of most telephone, Internet and mobile device systems. It uses standardized communication protocols that let mobile devices exchange short text messages. An intermediary service can facilitate a text-to-voice conversion to be sent to landlines.


title: SMS

text: SMS technology originated from radio telegraphy in radio memo pagers that used standardized phone protocols. These were defined in 1986 as part of the Global System for Mobile Communications (GSM) series of standards.<ref name="GSM 28/85">GSM Doc 28/85 "Services and Facilities to be provided in the GSM System" rev2, June 1985</ref> The first SMS message was sent on 3 December 1992, when Neil Papworth, a test engineer for Sema Group, sent "Merry Christmas" to the Orbitel 901 phone of colleague Richard Jarvis. SMS rolled out commercially on many cellular networks that decade and became hugely popular worldwide as a method of text communication. By the end of 2010, SMS was the most widely used data application, with an estimated 3.5 billion active users, or about 80% of all mobile phone subscribers.


title: SMS

text: The service allows users to send and receive messages of up to 160 characters (when entirely alpha-numeric) to and from GSM mobiles. Although most SMS messages are sent from one mobile phone to another, support for the service has expanded to include other mobile technologies, such as CDMA networks and Digital AMPS.


title: SMS

text: Mobile marketing, a type of direct marketing, uses SMS. The global SMS messaging business was estimated to be worth over US$240 billion in 2013, accounting for almost half of all revenue generated by mobile messaging.


title: SMS

text: Adding text messaging functionality to mobile devices began in the early 1980s. The first action plan of the CEPT Group GSM was approved in December 1982, requesting that "The services and facilities offered in the public switched telephone networks and public data networks ... should be available in the mobile system." This plan included the exchange of text messages either directly between mobile stations, or transmitted via message handling systems in use at that time.


title: SMS

text: The SMS concept was developed in the Franco-German GSM cooperation in 1984 by Friedhelm Hillebrand and Bernard Ghillebaert. The GSM is optimized for telephony, since this was identified as its main application. The key idea for SMS was to use this telephone-optimized system, and to transport messages on the signalling paths needed to control the telephone traffic during periods when no signalling traffic existed. In this way, unused resources in the system could be used to transport messages at minimal cost. However, it was necessary to limit the length of the messages to 128 bytes (later improved to 160 seven-bit characters) so that the messages could fit into the existing signalling formats. Based on his personal observations and on analysis of the typical lengths of postcard and Telex messages, Hillebrand argued that 160 characters was sufficient for most brief communications.


title: SMS

text: SMS could be implemented in every mobile station by updating its software. Hence, a large base of SMS-capable terminals and networks existed when people began to use SMS. A new network element required was a specialized short message service centre, and enhancements were required to the radio capacity and network transport infrastructure to accommodate growing SMS traffic.


title: SMS

text: The technical development of SMS was a multinational collaboration supporting the framework of standards bodies. Through these organizations the technology was made freely available to the whole world.


title: SMS

text: The first proposal which initiated the development of SMS was made by a contribution of Germany and France in the GSM group meeting in February 1985 in Oslo. This proposal was further elaborated in GSM subgroup WP1 Services (Chairman Martine Alvernhe, France Telecom) based on a contribution from Germany. There were also initial discussions in the subgroup WP3 network aspects chaired by Jan Audestad (Telenor). The result was approved by the main GSM group in a June 1985 document which was distributed to industry. The input documents on SMS had been prepared by Friedhelm Hillebrand of Deutsche Telekom, with contributions from Bernard Ghillebaert of France Télécom. The definition that Friedhelm Hillebrand and Bernard Ghillebaert brought into GSM called for the provision of a message transmission service of alphanumeric messages to mobile users "with acknowledgement capabilities". The last three words transformed SMS into something much more useful than the electronic paging services used at the time that some in GSM might have had in mind.


title: SMS

text: SMS was considered in the main GSM group as a possible service for the new digital cellular system. In GSM document ""Services and Facilities to be provided in the GSM System,"" both mobile-originated and mobile-terminated short messages appear on the table of GSM teleservices.


title: SMS

text: The discussions on the GSM services were concluded in the recommendation GSM 02.03 ""TeleServices supported by a GSM PLMN."" Here a rudimentary description of the three services was given:


title: SMS

text: The material elaborated in GSM and its WP1 subgroup was handed over in Spring 1987 to a new GSM body called IDEG (the Implementation of Data and Telematic Services Experts Group), which had its kickoff in May 1987 under the chairmanship of Friedhelm Hillebrand (German Telecom). The technical standard known today was largely created by IDEG (later WP4) as the two recommendations GSM 03.40 (the two point-to-point services merged) and GSM 03.41 (cell broadcast).


title: SMS

text: WP4 created a Drafting Group Message Handling (DGMH), which was responsible for the specification of SMS. Finn Trosby of Telenor chaired the draft group through its first 3 years, in which the design of SMS was established. DGMH had five to eight participants, and Finn Trosby mentions as major contributors Kevin Holley, Eija Altonen, Didier Luizard and Alan Cox. The first action plan mentions for the first time the Technical Specification 03.40 "Technical Realisation of the Short Message Service". Responsible editor was Finn Trosby. The first and very rudimentary draft of the technical specification was completed in November 1987. However, drafts useful for the manufacturers followed at a later stage in the period. A comprehensive description of the work in this period is given in.


title: SMS

text: The work on the draft specification continued in the following few years, where Kevin Holley of Cellnet (now Telefónica O2 UK) played a leading role. Besides the completion of the main specification GSM 03.40, the detailed protocol specifications on the system interfaces also needed to be completed.


title: SMS

text: The Mobile Application Part (MAP) of the SS7 protocol included support for the transport of Short Messages through the Core Network from its inception. MAP Phase 2 expanded support for SMS by introducing a separate operation code for Mobile Terminated Short Message transport. Since Phase 2, there have been no changes to the Short Message operation packages in MAP, although other operation packages have been enhanced to support CAMEL SMS control.


title: SMS

text: From 3GPP Releases 99 and 4 onwards, CAMEL Phase 3 introduced the ability for the Intelligent Network (IN) to control aspects of the Mobile Originated Short Message Service, while CAMEL Phase 4, as part of 3GPP Release 5 and onwards, provides the IN with the ability to control the Mobile Terminated service. CAMEL allows the gsmSCP to block the submission (MO) or delivery (MT) of Short Messages, route messages to destinations other than that specified by the user, and perform real-time billing for the use of the service. Prior to standardized CAMEL control of the Short Message Service, IN control relied on switch vendor specific extensions to the Intelligent Network Application Part (INAP) of SS7.


title: SMS

text: The first SMS message was sent over the Vodafone GSM network in the United Kingdom on 3 December 1992, from Neil Papworth of Sema Group (now Mavenir Systems) using a personal computer to Richard Jarvis of Vodafone using an Orbitel 901 handset. The text of the message was "Merry Christmas."


title: SMS

text: The first commercial deployment of a short message service center (SMSC) was by Aldiscon part of Logica (now part of CGI) with Telia (now TeliaSonera) in Sweden in 1993, followed by Fleet Call (now Nextel) in the US, Telenor in Norway and BT Cellnet (now O2 UK) later in 1993. All first installations of SMS gateways were for network notifications sent to mobile phones, usually to inform of voice mail messages.


title: SMS

text: The first commercially sold SMS service was offered to consumers, as a person-to-person text messaging service by Radiolinja (now part of Elisa) in Finland in 1993. Most early GSM mobile phone handsets did not support the ability to send SMS text messages, and Nokia was the only handset manufacturer whose total GSM phone line in 1993 supported user-sending of SMS text messages. According to Matti Makkonen, an engineer at Nokia at the time, the Nokia 2010, which was released in January 1994, was the first mobile phone to support composing SMSes easily.


title: SMS

text: Initial growth was slow, with customers in 1995 sending on average only 0.4 messages per GSM customer per month. One factor in the slow takeup of SMS was that operators were slow to set up charging systems, especially for prepaid subscribers, and eliminate billing fraud which was possible by changing SMSC settings on individual handsets to use the SMSCs of other operators. Initially, networks in the UK only allowed customers to send messages to other users on the same network, limiting the usefulness of the service. This restriction was lifted in 1999.


title: SMS

text: Over time, this issue was eliminated by switch billing instead of billing at the SMSC and by new features within SMSCs to allow blocking of foreign mobile users sending messages through it. By the end of 2000, the average number of messages reached 35 per user per month, and on Christmas Day 2006, over 205 million messages were sent in the UK alone.


title: SMS

text: SMS was originally designed as part of GSM, but is now available on a wide range of networks, including 3G networks. However, not all text messaging systems use SMS, and some notable alternative implementations of the concept include J-Phone's "SkyMail" and NTT Docomo's "Short Mail", both in Japan. Email messaging from phones, as popularized by NTT Docomo's i-mode and the RIM BlackBerry, also typically uses standard mail protocols such as SMTP over TCP/IP.


title: SMS

text: , 6.1 trillion (6.1 × 10) SMS text messages were sent, which is an average of 193,000 SMS per second. SMS has become a large commercial industry, earning $114.6 billion globally in 2010. The global average price for an SMS message is US$0.11, while mobile networks charge each other interconnect fees of at least US$0.04 when connecting between different phone networks.


title: SMS

text: In 2014, Caktus Group developed the world's first SMS-based voter registration system in Libya. As of February 2015 more than 1.5 million people have registered using that system, providing Libyan voters with unprecedented access to the democratic process.


title: SMS

text: SMS is being increasingly challenged by Internet Protocol-based messaging services such as RCS, Apple's iMessage, Signal, Facebook Messenger/WhatsApp, Telegram, Viber, WeChat (in China) and Line (in Japan), available on smart phones with internet connections.


title: SMS

text: SMS enablement allows individuals to send an SMS message to a business phone number (traditional landline) and receive a SMS in return. Providing customers with the ability to text to a phone number allows organizations to offer new services that deliver value. Examples include chat bots, and text enabled customer service and call centers.


title: SMS

text: The "Short Message Service—Point to Point (SMS-PP)"—was originally defined in GSM recommendation 03.40, which is now maintained in 3GPP as TS 23.040. GSM 03.41 (now 3GPP TS 23.041) defines the "Short Message Service—Cell Broadcast (SMS-CB)", which allows messages (advertising, public information, etc.) to be broadcast to all mobile users in a specified geographical area.


title: SMS

text: Messages are sent to a short message service center (SMSC), which provides a "store and forward" mechanism. It attempts to send messages to the SMSC's recipients. If a recipient is not reachable, the SMSC queues the message for later retry. Some SMSCs also provide a "forward and forget" option where transmission is tried only once. Both mobile terminated (MT, for messages sent "to" a mobile handset) and mobile originating (MO, for those sent "from" the mobile handset) operations are supported. Message delivery is "best effort", so there are no guarantees that a message will actually be delivered to its recipient, but delay or complete loss of a message is uncommon, typically affecting less than 5 percent of messages. Some providers allow users to request delivery reports, either via the SMS settings of most modern phones, or by prefixing each message with *0# or *N#. However, the exact meaning of confirmations varies from reaching the network, to being queued for sending, to being sent, to receiving a confirmation of receipt from the target device, and users are often not informed of the specific type of success being reported.


title: SMS

text: SMS is a stateless communication protocol in which every SMS message is considered entirely independent of other messages. Enterprise applications using SMS as a communication channel for stateful dialogue (where an MO reply message is paired to a specific MT message) requires that session management be maintained external to the protocol.


title: SMS

text: Transmission of short messages between the SMSC and the handset is done whenever using the Mobile Application Part (MAP) of the SS7 protocol. Messages are sent with the MAP MO- and MT-ForwardSM operations, whose payload length is limited by the constraints of the signaling protocol to precisely 140 bytes (140 bytes * 8 bits / byte = 1120 bits).


title: SMS

text: Short messages can be encoded using a variety of alphabets: the default GSM 7-bit alphabet, the 8-bit data alphabet, and the 16-bit UCS-2 alphabet. Depending on which alphabet the subscriber has configured in the handset, this leads to the maximum individual short message sizes of 160 7-bit characters, 140 8-bit characters, or 70 16-bit characters. GSM 7-bit alphabet support is mandatory for GSM handsets and network elements, but characters in languages such as Hindi, Arabic, Chinese, Korean, Japanese, or Cyrillic alphabet languages (e.g., Russian, Ukrainian, Serbian, Bulgarian, etc.) must be encoded using the 16-bit UCS-2 character encoding (see Unicode). Routing data and other metadata is additional to the payload size.


title: SMS

text: Larger content (concatenated SMS, multipart or segmented SMS, or "long SMS") can be sent using multiple messages, in which case each message will start with a User Data Header (UDH) containing segmentation information. Since UDH is part of the payload, the number of available characters per segment is lower: 153 for 7-bit encoding, 134 for 8-bit encoding and 67 for 16-bit encoding. The receiving handset is then responsible for reassembling the message and presenting it to the user as one long message. While the standard theoretically permits up to 255 segments, 10 segments is the practical maximum with some carriers, and long messages are often billed as equivalent to multiple SMS messages. In some cases 127 segments are supported, but software limitations in some SMS applications do not permit this. Some providers have offered length-oriented pricing schemes for messages, although that type of pricing structure is rapidly disappearing.


title: SMS

text: SMS gateway providers facilitate SMS traffic between businesses and mobile subscribers, including SMS for enterprises, content delivery, and entertainment services involving SMS, e.g. TV voting. Considering SMS messaging performance and cost, as well as the level of messaging services, SMS gateway providers can be classified as aggregators or SS7 providers.


title: SMS

text: The aggregator model is based on multiple agreements with mobile carriers to exchange two-way SMS traffic into and out of the operator's SMSC, also known as "local termination model". Aggregators lack direct access into the SS7 protocol, which is the protocol where the SMS messages are exchanged. SMS messages are delivered to the operator's SMSC, but not the subscriber's handset; the SMSC takes care of further handling of the message through the SS7 network.


title: SMS

text: Another type of SMS gateway provider is based on SS7 connectivity to route SMS messages, also known as "international termination model". The advantage of this model is the ability to route data directly through SS7, which gives the provider total control and visibility of the complete path during SMS routing. This means SMS messages can be sent directly to and from recipients without having to go through the SMSCs of other mobile operators. Therefore, it is possible to avoid delays and message losses, offering full delivery guarantees of messages and optimized routing. This model is particularly efficient when used in mission-critical messaging and SMS used in corporate communications. Moreover, these SMS gateway providers are providing branded SMS services with masking but after misuse of these gateways most countries' governments have taken serious steps to block these gateways.


title: SMS

text: Message Service Centers communicate with the Public Land Mobile Network (PLMN) or PSTN via Interworking and Gateway MSCs.


title: SMS

text: Subscriber-originated messages are transported from a handset to a service center, and may be destined for mobile users, subscribers on a fixed network, or Value-Added Service Providers (VASPs), also known as application-terminated. Subscriber-terminated messages are transported from the service center to the destination handset, and may originate from mobile users, from fixed network subscribers, or from other sources such as VASPs.


title: SMS

text: On some carriers nonsubscribers can send messages to a subscriber's phone using an Email-to-SMS gateway. Additionally, many carriers, including AT&T Mobility, T-Mobile USA, Sprint, and Verizon Wireless, offer the ability to do this through their respective websites.


title: SMS

text: For example, an AT&T subscriber whose phone number was 555-555-5555 would receive emails addressed to 5555555555@txt.att.net as text messages. Subscribers can easily reply to these SMS messages, and the SMS reply is sent back to the original email address. Sending email to SMS is free for the sender, but the recipient is subject to the standard delivery charges. Only the first 160 characters of an email message can be delivered to a phone, and only 160 characters can be sent from a phone. However, longer messages may be broken up into multiple texts, depending upon the telephone service provider.


title: SMS

text: Text-enabled fixed-line handsets are required to receive messages in text format. However, messages can be delivered to non enabled phones using text-to-speech conversion.


title: SMS

text: Short messages can send binary content such as ringtones or logos, as well as Over-the-air programming (OTA) or configuration data. Such uses are a vendor-specific extension of the GSM specification and there are multiple competing standards, although Nokia's Smart Messaging is common. An alternative way for sending such binary content is EMS messaging, which is standardized and not dependent on vendors.


title: SMS

text: SMS is used for M2M (Machine to Machine) communication. For instance, there is an LED display machine controlled by SMS, and some vehicle tracking companies use SMS for their data transport or telemetry needs. SMS usage for these purposes is slowly being superseded by GPRS services owing to their lower overall cost. GPRS is offered by smaller telco players as a route of sending SMS text to reduce the cost of SMS texting internationally.


title: SMS

text: Many mobile and satellite transceiver units support the sending and receiving of SMS using an extended version of the Hayes command set. The extensions were standardised as part of the GSM Standards and extended as part of the 3GPP standards process.


title: SMS

text: The connection between the terminal equipment and the transceiver can be realized with a serial cable (e.g., USB), a Bluetooth link, an infrared link, etc. Common AT commands include AT+CMGS (send message), AT+CMSS (send message from storage), AT+CMGL (list messages) and AT+CMGR (read message).


title: SMS

text: However, not all modern devices support receiving of messages if the message storage (for instance the device's internal memory) is not accessible using AT commands.


title: SMS

text: Short messages may be used normally to provide premium rate services to subscribers of a telephone network.


title: SMS

text: Mobile-terminated short messages can be used to deliver digital content such as news alerts, financial information, logos, and ring tones. The first premium-rate media content delivered via the SMS system was the world's first paid downloadable ringing tones, as commercially launched by Saunalahti (later Jippii Group, now part of Elisa Group), in 1998. Initially, only Nokia branded phones could handle them. By 2002 the ringtone business globally had exceeded $1 billion of service revenues, and nearly US$5 billion by 2008. Today, they are also used to pay smaller payments online—for example, for file-sharing services, in mobile application stores, or VIP section entrance. Outside the online world, one can buy a bus ticket or beverages from ATM, pay a parking ticket, order a store catalog or some goods (e.g., discount movie DVDs), make a donation to charity, and much more.


title: SMS

text: The Value-added service provider (VASP) providing the content submits the message to the mobile operator's SMSC(s) using a TCP/IP protocol such as the short message peer-to-peer protocol (SMPP) or the External Machine Interface (EMI). The SMSC delivers the text using the normal Mobile Terminated delivery procedure. The subscribers are charged extra for receiving this premium content; the revenue is typically divided between the mobile network operator and the VASP either through revenue share or a fixed transport fee. Submission to the SMSC is usually handled by a third party.


title: SMS

text: Mobile-originated short messages may also be used in a premium-rated manner for services such as televoting. In this case, the VASP providing the service obtains a short code from the telephone network operator, and subscribers send texts to that number. The payouts to the carriers vary by carrier; percentages paid are greatest on the lowest-priced premium SMS services. Most information providers should expect to pay about 45 percent of the cost of the premium SMS up front to the carrier. The submission of the text to the SMSC is identical to a standard MO Short Message submission, but once the text is at the SMSC, the Service Center (SC) identifies the Short Code as a premium service. The SC will then direct the content of the text message to the VASP, typically using an IP protocol such as SMPP or EMI. Subscribers are charged a premium for the sending of such messages, with the revenue typically shared between the network operator and the VASP. Short codes only work within one country, they are not international.


title: SMS

text: An alternative to inbound SMS is based on long numbers (international number format, such as "+44 762 480 5000"), which can be used in place of short codes for SMS reception in several applications, such as TV voting, product promotions and campaigns. Long numbers work internationally, allow businesses to use their own numbers, rather than short codes, which are usually shared across many brands. Additionally, long numbers are nonpremium inbound numbers.


title: SMS

text: Threaded SMS is a visual styling orientation of SMS message history that arranges messages to and from a contact in chronological order on a single screen.


title: SMS

text: It was first invented by a developer working to implement the SMS client for the BlackBerry, who was looking to make use of the blank screen left below the message on a device with a larger screen capable of displaying far more than the usual 160 characters, and was inspired by threaded Reply conversations in email.


title: SMS

text: Visually, this style of representation provides a back-and-forth chat-like history for each individual contact. Hierarchical-threading at the conversation-level (as typical in blogs and on-line messaging boards) is not widely supported by SMS messaging clients. This limitation is due to the fact that there is no session identifier or subject-line passed back and forth between sent and received messages in the header data (as specified by SMS protocol) from which the client device can properly thread an incoming message to a specific dialogue, or even to a specific message within a dialogue.


title: SMS

text: Most smart phone text-messaging-clients are able to create some contextual threading of "group messages" which narrows the context of the thread around the common interests shared by group members. On the other hand, advanced enterprise messaging applications which push messages from a remote server often display a dynamically changing reply number (multiple numbers used by the same sender), which is used along with the sender's phone number to create session-tracking capabilities analogous to the functionality that cookies provide for web-browsing. As one pervasive example, this technique is used to extend the functionality of many Instant Messenger (IM) applications such that they are able to communicate over two-way dialogues with the much larger SMS user-base. In cases where multiple reply numbers are used by the enterprise server to maintain the dialogue, the visual conversation threading on the client may be separated into multiple threads.


title: SMS

text: While SMS reached its popularity as a person-to-person messaging, another type of SMS is growing fast: application-to-person (A2P) messaging. A2P is a type of SMS sent from a subscriber to an application or sent from an application to a subscriber. It is commonly used by businesses, such as banks, e-gaming, logistic companies, e-commerce, to send SMS messages from their systems to their customers.


title: SMS

text: In the US, carriers have traditionally preferred that A2P messages must be sent using a short code rather than a standard long code. However, recently multiple US carriers, including Verizon have announced plans to officially support A2P messages over long codes. In the United Kingdom A2P messages can be sent with a dynamic 11 character sender ID; however, short codes are used for OPTOUT commands.


title: SMS

text: All commercial satellite phone networks except ACeS and OptusSat support SMS. While early Iridium handsets only support incoming SMS, later models can also send messages. The price per message varies for different networks. Unlike some mobile phone networks, there is no extra charge for sending international SMS or to send one to a different satellite phone network. SMS can sometimes be sent from areas where the signal is too poor to make a voice call.


title: SMS

text: Satellite phone networks usually have web-based or email-based SMS portals where one can send free SMS to phones on that particular network.


title: SMS

text: Unlike dedicated texting systems like the Simple Network Paging Protocol and Motorola's ReFLEX protocol, SMS message delivery is not guaranteed, and many implementations provide no mechanism through which a sender can determine whether an SMS message has been delivered in a timely manner. SMS messages are generally treated as lower-priority traffic than voice, and various studies have shown that around 1% to 5% of messages are lost entirely, even during normal operation conditions, and others may not be delivered until long after their relevance has passed. The use of SMS as an emergency notification service in particular has been questioned.


title: SMS

text: The Global Service for Mobile communications (GSM), with the greatest worldwide number of users, succumbs to several security vulnerabilities. In the GSM, only the airway traffic between the Mobile Station (MS) and the Base Transceiver Station (BTS) is optionally encrypted with a weak and broken stream cipher (A5/1 or A5/2). The authentication is unilateral and also vulnerable. There are also many other security vulnerabilities and shortcomings. Such vulnerabilities are inherent to SMS as one of the superior and well-tried services with a global availability in the GSM networks. SMS messaging has some extra security vulnerabilities due to its store-and-forward feature, and the problem of fake SMS that can be conducted via the Internet. When a user is roaming, SMS content passes through different networks, perhaps including the Internet, and is exposed to various vulnerabilities and attacks. Another concern arises when an adversary gets access to a phone and reads the previous unprotected messages.


title: SMS

text: In October 2005, researchers from Pennsylvania State University published an analysis of vulnerabilities in SMS-capable cellular networks. The researchers speculated that attackers might exploit the open functionality of these networks to disrupt them or cause them to fail, possibly on a nationwide scale.


title: SMS

text: The GSM industry has identified a number of potential fraud attacks on mobile operators that can be delivered via abuse of SMS messaging services. The most serious threat is SMS Spoofing, which occurs when a fraudster manipulates address information in order to impersonate a user that has roamed onto a foreign network and is submitting messages to the home network. Frequently, these messages are addressed to destinations outside the home network—with the home SMSC essentially being "hijacked" to send messages into other networks.


title: SMS

text: The only sure way of detecting and blocking spoofed messages is to screen incoming mobile-originated messages to verify that the sender is a valid subscriber and that the message is coming from a valid and correct location. This can be implemented by adding an intelligent routing function to the network that can query originating subscriber details from the home location register (HLR) before the message is submitted for delivery. This kind of intelligent routing function is beyond the capabilities of legacy messaging infrastructure.


title: SMS

text: In an effort to limit telemarketers who had taken to bombarding users with hordes of unsolicited messages, India introduced new regulations in September 2011, including a cap of 3,000 SMS messages per subscriber per month, or an average of 100 per subscriber per day. Due to representations received from some of the service providers and consumers, TRAI (Telecom Regulatory Authority of India) has raised this limit to 200 SMS messages per SIM per day in case of prepaid services, and up to 6,000 SMS messages per SIM per month in case of postpaid services with effect from November 1, 2011. However, it was ruled unconstitutional by the Delhi high court, but there are some limitations.


title: SMS

text: A Flash SMS is a type of SMS that appears directly on the main screen without user interaction and is not automatically stored in the inbox. It can be useful in emergencies, such as a fire alarm or cases of confidentiality, as in delivering one-time passwords.


title: SMS

text: In 2010 Germany, almost half a million "silent SMS" messages were sent by the federal police, customs and the secret service "Verfassungsschutz" (offices for protection of the constitution). These silent messages, also known as "silent TMS", "stealth SMS", "stealth ping" or "Short Message Type 0", are used to locate a person and thus to create a complete movement profile. They do not show up on a display, nor trigger any acoustical signal when received. Their primary purpose was to deliver special services of the network operator to any cell phone.


title: Pat Sajak

text: Pat Sajak ( , born Patrick Leonard ; born October 26, 1946) is an American television personality and game show host. He is best known as the host of the American television game show "Wheel of Fortune", a position he has held since 1981. For his work on "Wheel", Sajak has received 19 nominations for the Daytime Emmy Award for Outstanding Game Show Host, winning three times.


title: Pat Sajak

text: Born in Chicago, Illinois, on October 26, 1946, Sajak graduated from Farragut High School in 1964, then went to Columbia College Chicago while working as a desk clerk at the Palmer House hotel.


title: Pat Sajak

text: He served in the U.S. Army as a disc jockey during the Vietnam War for American Forces Vietnam Network. Sajak hosted the same "Dawn Buster" radio show that Adrian Cronauer had, and for 14 months followed Cronauer's tradition of signing on with "Good Morning Vietnam!"


title: Pat Sajak

text: Sajak won a contest on WLS radio's "Dick Biondi Show" to be a guest teen deejay. While at Columbia College Chicago, his broadcasting instructor Al Parker told him that a local radio station (WEDC) was looking for a newsman. Sajak applied for the job and was hired to work from midnight to 6:00 am. In 1968, he joined the U.S. Army and was sent to Vietnam, where he served as a disc jockey on Armed Forces Radio. On the Military Channel's program, "An Officer and a Movie", Sajak admitted to botching President Richard Nixon's 1969 Christmas broadcast to the troops; he accidentally cut the feed off prematurely. Upon realizing the error, Sajak decided it would be best not to resume the feed. In the early 1970s, he DJed for a year for a Murray, Kentucky radio station. Also in the early 1970s, Sajak began DJing at 50,000-watt WSM in Nashville; at the time, WSM was playing pop music during the day, and he was the 2:30–5:00 pm afternoon personality. The radio station's television sister, WSM-TV (now WSMV), brought Sajak on screen, first as a voiceover artist making station identifications and anchoring the five-minute newscasts during NBC's "Today Show", then as a weekend and substitute weatherman, where he became acquainted with anchor Dan Miller. In 1977, KNBC-TV in Los Angeles was looking for a weather reporter and spotted Sajak working in Nashville. He accepted KNBC's request for him to be a full-time weather reporter for the station.


title: Pat Sajak

text: In 1981, Merv Griffin asked Sajak if he would be interested in taking over the duties as host on "Wheel of Fortune" from Chuck Woolery. However, Fred Silverman, the president and CEO of NBC, rejected his hiring, claiming Sajak was too local, and Griffin responded by imposing a moratorium on new tapings until Sajak was hired. The issue became moot when Silverman was dismissed due to repeated programming failures and replaced by Brandon Tartikoff. Sajak, who had already hosted two game show pilots in 1980, "Press Your Luck" for Ralph Edwards (no relation to the 1983 CBS game show of the same name) and "Puzzlers" for Mark Goodson, accepted the position. Sajak hosted both the daytime (NBC) and syndicated evening versions of "Wheel" from 1983 to 1989 and continues to host the latter version. With Sajak returning for his 36th season in 2018–19, he became the longest-running host of any game show, surpassing Bob Barker, who hosted "The Price Is Right" from 1972 to 2007. Sajak was officially honored as such by the Guinness World Records with the episode taped on March 28, 2019, and aired May 8, 2019 (two days before the primetime version's 7,000th episode).


title: Pat Sajak

text: Sajak had a small role as a Buffalo, New York newscaster in the 1982 comedy film "." When his late-night talk show on CBS premiered in January 1989, he left the daytime version of "Wheel" and was replaced by former San Diego Chargers place-kicker Rolf Benirschke (who was later replaced by Bob Goen when the daytime show moved to CBS in July of that year). Sajak appeared on "Super Password" several times from 1984 to 1989, as well as "Password Plus" in 1981, shortly before taking on hosting duties on "Wheel". Other game shows on which he appeared as a celebrity guest were "Dream House", "Just Men!", and "Match Game-Hollywood Squares Hour".


title: Pat Sajak

text: Sajak hosted a short-lived late-night talk show on CBS from January 9, 1989, to April 13, 1990. Dan Miller, Sajak's old friend and former anchor at WSM-TV in Nashville, joined him as his sidekick. Sajak later became a frequent guest host for CNN's "Larry King Live" when King was unable to do the show. He became a regular substitute host for Regis Philbin on the syndicated "Live with Regis and Kelly". Sajak also hosted "Pat Sajak Weekend" on Fox News in 2003. From at least 2002, Sajak hosted "The Pat Sajak Baseball Hour", a syndicated weekly radio sports talk show that ended in 2006 due to scheduling conflicts.


title: Pat Sajak

text: Sajak is an external director of conservative publishing house Eagle Publishing. He has served on the board of directors for the Claremont Institute.


title: Pat Sajak

text: In 1997, Sajak pulled an April Fool's Day prank on fans when Vanna White and he were contestants on an episode of "Wheel" hosted by Alex Trebek. The winnings of both Sajak and White were donated to charity (in this case, the American Cancer Society and the Boy Scouts of America). In return, Sajak hosted a regular episode of "Jeopardy!" in place of Trebek. Sajak also appeared at the beginning of a 2010 April Fool's episode, along with Jeff Probst and Neil Patrick Harris.


title: Pat Sajak

text: Sajak began writing for the "National Review Online" in 2010. In his first post, he questioned whether public employees should be allowed to vote on issues that would benefit them directly. He also has contributed to the center-right sociopolitical / social networking website Ricochet.com.


title: Pat Sajak

text: Sajak is the author of several puzzle games, the first and best-known of them being "Lucky Letters", which debuted in 2007. The games, which Sajak developed with puzzle developer David L. Hoyt, are syndicated through Universal Uclick.


title: Pat Sajak

text: Sajak has appeared on episodes of ESPN Radio's "The Dan Le Batard Show with Stugotz", as well as Le Batard's other show, "Highly Questionable".


title: Pat Sajak

text: Since 2020, Sajak has been credited as a Consulting Producer (since the start of Season 39) of "Wheel of Fortune".


title: Pat Sajak

text: In September 2021, it was announced that both Sajak and White had signed on to continue as hosts of "Wheel of Fortune" through the 2023–24 season. In 2021, Sajak voiced a singing bust in a "Muppets Haunted Mansion" television special.


title: Pat Sajak

text: Sajak was parodied in a 1980s "Sesame Street" sketch, with a Muppet named Pat Playjacks hosting "Squeal of Fortune". The goal was for the contestants (Prairie Dawn and The Count) to guess how many times a pig in the center of the wheel would squeal before the wheel stopped.


title: Pat Sajak

text: During the 1980s, comedian Martin Short frequently portrayed a fictional character he called Ed Grimley, a hyperactive manchild who is obsessed with banal popular culture – Sajak in particular – on the sketch comedy television shows "SCTV" and "Saturday Night Live".


title: Pat Sajak

text: In 1986, Sajak and his "Wheel of Fortune" co-star Vanna White portrayed themselves on an episode of the NBC sitcom "227".


title: Pat Sajak

text: In the fourth-season episode of "The A-Team" called "Wheel of Fortune", Sajak makes a cameo along with co-star Vanna White. In the episode, Murdock wins big at "Wheel of Fortune" due to Face's system of guessing the letters correctly.


title: Pat Sajak

text: In 1992, Sajak was a special guest star in the TV show "The Commish". The episode first aired on November 7, 1992, and was called "The Two Faces of Ed". He played psychologist Brian Brandon.


title: Pat Sajak

text: In the fourth episode of season three of Comedy Central's "Brickleberry", "That Brother's My Father", Sajak gets kidnapped and becomes a hostage to the wheel of fortune.


title: Pat Sajak

text: Sajak is married to Lesly Brown-Sajak, a photographer, with whom he has a son, Patrick Michael James Sajak (born September 22, 1990), and a daughter, Maggie Marie Sajak (born January 5, 1995). The couple lives in Severna Park, Maryland, with a second home in Los Angeles, California.


title: Pat Sajak

text: In 2005, Sajak became an investor in the Golden Baseball League, an independent professional baseball league with teams in California, Arizona, Nevada, Utah, Alberta, British Columbia, and Baja California. During a guest appearance in the broadcast booth at a March 2012 Baltimore Orioles – Boston Red Sox spring-training game, Sajak acknowledged that he had called some baseball games in the past.


title: Pat Sajak

text: Sajak is featured in a brief film shown at the visitor's center at Mount Vernon, the residence of George Washington, where he explains to tourists the attractions of the site. Sajak, since 1998, owns Maryland-based AM radio station WNAV in Annapolis.


title: Pat Sajak

text: Sajak is a Republican, and has written a number of columns for the conservative magazine "Human Events". He is also a regular poster and podcast participant on the conservative blog Ricochet.com. Sajak considers himself a climate change skeptic. He is also a financial supporter of the Young America's Foundation, which sponsors conservative speakers on college campuses.


title: Pat Sajak

text: In 2019, Sajak began serving as the Hillsdale College board of trustees chair. He previously served as vice-chair for 15 years.


title: Pat Sajak

text: Sajak is an avid fan of the Washington Capitals NHL team. He is a longtime season-ticket holder and made an on-ice appearance before game three of the 2018 Stanley Cup Finals.


title: Pat Sajak

text: Sajak underwent emergency intestinal surgery to remove a blockage on November 8, 2019. While Sajak recovered, co-host Vanna White hosted in his place. The first taping day in which he was incapacitated was a Disney-themed Christmas episode week. Disney characters took over White's role at the puzzle board for that week. Sajak's daughter Maggie also helped White for a week.


title: Momentum

text: In Newtonian mechanics, momentum (more specifically linear momentum or translational momentum) is the product of the mass and velocity of an object. It is a standard mechanical quantity. It is a vector quantity, possessing a magnitude and a direction. If is an object's mass and is its velocity (also a vector quantity), then the object's momentum is : formula_1


title: Momentum

text: In the International System of Units (SI), the unit of measurement of momentum is the kilogram metre per second (kg⋅m/s), which is equivalent to the newton-second.


title: Momentum

text: Newton's second law of motion states that the rate of change of a body's momentum is equal to the net force acting on it. Momentum depends on the frame of reference, but in any inertial frame it is a "conserved" quantity, meaning that if a closed system is not affected by external forces, its total linear momentum does not change. Momentum is also conserved in special relativity (with a modified formula) and, in a modified form, in electrodynamics, quantum mechanics, quantum field theory, and general relativity. It is an expression of one of the fundamental symmetries of space and time: translational symmetry.


title: Momentum

text: Advanced formulations of classical mechanics, Lagrangian and Hamiltonian mechanics, allow one to choose coordinate systems that incorporate symmetries and constraints. In these systems the conserved quantity is generalized momentum, and in general this is different from the kinetic momentum defined above. The concept of generalized momentum is carried over into quantum mechanics, where it becomes an operator on a wave function. The momentum and position operators are related by the Heisenberg uncertainty principle.


title: Momentum

text: In continuous systems such as electromagnetic fields, fluid dynamics and deformable bodies, a momentum density can be defined, and a continuum version of the conservation of momentum leads to equations such as the Navier–Stokes equations for fluids or the Cauchy momentum equation for deformable solids or fluids.


title: Momentum

text: Momentum is a vector quantity: it has both magnitude and direction. Since momentum has a direction, it can be used to predict the resulting direction and speed of motion of objects after they collide. Below, the basic properties of momentum are described in one dimension. The vector equations are almost identical to the scalar equations (see multiple dimensions).


title: Momentum

text: The momentum of a particle is conventionally represented by the letter . It is the product of two quantities, the particle's mass (represented by the letter ) and its velocity ():


title: Momentum

text: The unit of momentum is the product of the units of mass and velocity. In SI units, if the mass is in kilograms and the velocity is in meters per second then the momentum is in kilogram meters per second (kg⋅m/s). In cgs units, if the mass is in grams and the velocity in centimeters per second, then the momentum is in gram centimeters per second (g⋅cm/s).


title: Momentum

text: Being a vector, momentum has magnitude and direction. For example, a 1 kg model airplane, traveling due north at 1 m/s in straight and level flight, has a momentum of 1 kg⋅m/s due north measured with reference to the ground.


title: Momentum

text: The momentum of a system of particles is the vector sum of their momenta. If two particles have respective masses and , and velocities and , the total momentum is


title: Momentum

text: A system of particles has a center of mass, a point determined by the weighted sum of their positions:


title: Momentum

text: If one or more of the particles is moving, the center of mass of the system will generally be moving as well (unless the system is in pure rotation around it). If the total mass of the particles is formula_6, and the center of mass is moving at velocity , the momentum of the system is:


title: Momentum

text: If the net force applied to a particle is constant, and is applied for a time interval , the momentum of the particle changes by an amount


title: Momentum

text: In differential form, this is Newton's second law; the rate of change of the momentum of a particle is equal to the instantaneous force acting on it,


title: Momentum

text: If the net force experienced by a particle changes as a function of time, , the change in momentum (or impulse ) between times and is


title: Momentum

text: Impulse is measured in the derived units of the newton second (1 N⋅s = 1 kg⋅m/s) or dyne second (1 dyne⋅s = 1 g⋅cm/s)


title: Momentum

text: "Example": A model airplane of mass 1 kg accelerates from rest to a velocity of 6 m/s due north in 2 s. The net force required to produce this acceleration is 3 newtons due north. The change in momentum is 6 kg⋅m/s due north. The rate of change of momentum is 3 (kg⋅m/s)/s due north which is numerically equivalent to 3 newtons.


title: Momentum

text: In a closed system (one that does not exchange any matter with its surroundings and is not acted on by external forces) the total momentum remains constant. This fact, known as the "law of conservation of momentum", is implied by Newton's laws of motion. Suppose, for example, that two particles interact. As explained by the third law, the forces between them are equal in magnitude but opposite in direction. If the particles are numbered 1 and 2, the second law states that and . Therefore,


title: Momentum

text: If the velocities of the particles are and before the interaction, and afterwards they are and , then


title: Momentum

text: This law holds no matter how complicated the force is between particles. Similarly, if there are several particles, the momentum exchanged between each pair of particles adds to zero, so the total change in momentum is zero. This conservation law applies to all interactions, including collisions (both elastic and inelastic) and separations caused by explosive forces. It can also be generalized to situations where Newton's laws do not hold, for example in the theory of relativity and in electrodynamics.


title: Momentum

text: Momentum is a measurable quantity, and the measurement depends on the frame of reference. For example: if an aircraft of mass 1000 kg is flying through the air at a speed of 50 m/s its momentum can be calculated to be 50,000 kg.m/s. If the aircraft is flying into a headwind of 5 m/s its speed relative to the surface of the Earth is only 45 m/s and its momentum can be calculated to be 45,000 kg.m/s. Both calculations are equally correct. In both frames of reference, any change in momentum will be found to be consistent with the relevant laws of physics.


title: Momentum

text: Suppose is a position in an inertial frame of reference. From the point of view of another frame of reference, moving at a constant speed relative to the other, the position (represented by a primed coordinate) changes with time as


title: Momentum

text: If a particle is moving at speed in the first frame of reference, in the second, it is moving at speed


title: Momentum

text: Since does not change, the second reference frame is also an inertial frame and the accelerations are the same:


title: Momentum

text: Thus, momentum is conserved in both reference frames. Moreover, as long as the force has the same form, in both frames, Newton's second law is unchanged. Forces such as Newtonian gravity, which depend only on the scalar distance between objects, satisfy this criterion. This independence of reference frame is called Newtonian relativity or Galilean invariance.


title: Momentum

text: A change of reference frame, can, often, simplify calculations of motion. For example, in a collision of two particles, a reference frame can be chosen, where, one particle begins at rest. Another, commonly used reference frame, is the center of mass frame – one that is moving with the center of mass. In this frame,


title: Momentum

text: If two particles, each of known momentum, collide and coalesce, the law of conservation of momentum can be used to determine the momentum of the coalesced body. If the outcome of the collision is that the two particles separate, the law is not sufficient to determine the momentum of each particle. If the momentum of one particle after the collision is known, the law can be used to determine the momentum of the other particle. Alternatively if the combined kinetic energy after the collision is known, the law can be used to determine the momentum of each particle after the collision. Kinetic energy is usually not conserved. If it is conserved, the collision is called an "elastic collision"; if not, it is an "inelastic collision".


title: Momentum

text: An elastic collision is one in which no kinetic energy is transformed into heat or some other form of energy. Perfectly elastic collisions can occur when the objects do not touch each other, as for example in atomic or nuclear scattering where electric repulsion keeps the objects apart. A slingshot maneuver of a satellite around a planet can also be viewed as a perfectly elastic collision. A collision between two pool balls is a good example of an "almost" totally elastic collision, due to their high rigidity, but when bodies come in contact there is always some dissipation.


title: Momentum

text: A head-on elastic collision between two bodies can be represented by velocities in one dimension, along a line passing through the bodies. If the velocities are and before the collision and and after, the equations expressing conservation of momentum and kinetic energy are:


title: Momentum

text: A change of reference frame can simplify analysis of a collision. For example, suppose there are two bodies of equal mass , one stationary and one approaching the other at a speed (as in the figure). The center of mass is moving at speed and both bodies are moving towards it at speed . Because of the symmetry, after the collision both must be moving away from the center of mass at the same speed. Adding the speed of the center of mass to both, we find that the body that was moving is now stopped and the other is moving away at speed . The bodies have exchanged their velocities. Regardless of the velocities of the bodies, a switch to the center of mass frame leads us to the same conclusion. Therefore, the final velocities are given by


title: Momentum

text: If one body has much greater mass than the other, its velocity will be little affected by a collision while the other body will experience a large change.


title: Momentum

text: In an inelastic collision, some of the kinetic energy of the colliding bodies is converted into other forms of energy (such as heat or sound). Examples include traffic collisions, in which the effect of loss of kinetic energy can be seen in the damage to the vehicles; electrons losing some of their energy to atoms (as in the Franck–Hertz experiment); and particle accelerators in which the kinetic energy is converted into mass in the form of new particles.


title: Momentum

text: In a perfectly inelastic collision (such as a bug hitting a windshield), both bodies have the same motion afterwards. A head-on inelastic collision between two bodies can be represented by velocities in one dimension, along a line passing through the bodies. If the velocities are and before the collision then in a perfectly inelastic collision both bodies will be travelling with velocity after the collision. The equation expressing conservation of momentum is:


title: Momentum

text: If one body is motionless to begin with (e.g. formula_23), the equation for conservation of momentum is


title: Momentum

text: In a different situation, if the frame of reference is moving at the final velocity such that formula_26, the objects would be brought to rest by a perfectly inelastic collision and 100% of the kinetic energy is converted to other forms of energy. In this instance the initial velocities of the bodies would be non-zero, or the bodies would have to be massless.


title: Momentum

text: One measure of the inelasticity of the collision is the coefficient of restitution , defined as the ratio of relative velocity of separation to relative velocity of approach. In applying this measure to a ball bouncing from a solid surface, this can be easily measured using the following formula:


title: Momentum

text: The momentum and energy equations also apply to the motions of objects that begin together and then move apart. For example, an explosion is the result of a chain reaction that transforms potential energy stored in chemical, mechanical, or nuclear form into kinetic energy, acoustic energy, and electromagnetic radiation. Rockets also make use of conservation of momentum: propellant is thrust outward, gaining momentum, and an equal and opposite momentum is imparted to the rocket.


title: Momentum

text: Real motion has both direction and velocity and must be represented by a vector. In a coordinate system with axes, velocity has components in the -direction, in the -direction, in the -direction. The vector is represented by a boldface symbol:


title: Momentum

text: The equations in the previous sections, work in vector form if the scalars and are replaced by vectors and . Each vector equation represents three scalar equations. For example,


title: Momentum

text: The kinetic energy equations are exceptions to the above replacement rule. The equations are still one-dimensional, but each scalar represents the magnitude of the vector, for example,


title: Momentum

text: Each vector equation represents three scalar equations. Often coordinates can be chosen so that only two components are needed, as in the figure. Each component can be obtained separately and the results combined to produce a vector result.


title: Momentum

text: A simple construction involving the center of mass frame can be used to show that if a stationary elastic sphere is struck by a moving sphere, the two will head off at right angles after the collision (as in the figure).


title: Momentum

text: The concept of momentum plays a fundamental role in explaining the behavior of variable-mass objects such as a rocket ejecting fuel or a star accreting gas. In analyzing such an object, one treats the object's mass as a function that varies with time: . The momentum of the object at time is therefore . One might then try to invoke Newton's second law of motion by saying that the external force on the object is related to its momentum by , but this is incorrect, as is the related expression found by applying the product rule to :


title: Momentum

text: This equation does not correctly describe the motion of variable-mass objects. The correct equation is


title: Momentum

text: where is the velocity of the ejected/accreted mass "as seen in the object's rest frame". This is distinct from , which is the velocity of the object itself as seen in an inertial frame.


title: Momentum

text: This equation is derived by keeping track of both the momentum of the object as well as the momentum of the ejected/accreted mass ("dm"). When considered together, the object and the mass ("dm") constitute a closed system in which total momentum is conserved.


title: Momentum

text: Newtonian physics assumes that absolute time and space exist outside of any observer; this gives rise to Galilean invariance. It also results in a prediction that the speed of light can vary from one reference frame to another. This is contrary to observation. In the special theory of relativity, Einstein keeps the postulate that the equations of motion do not depend on the reference frame, but assumes that the speed of light is invariant. As a result, position and time in two reference frames are related by the Lorentz transformation instead of the Galilean transformation.


title: Momentum

text: Consider, for example, one reference frame moving relative to another at velocity in the direction. The Galilean transformation gives the coordinates of the moving frame as


title: Momentum

text: Newton's second law, with mass fixed, is not invariant under a Lorentz transformation. However, it can be made invariant by making the "inertial mass" of an object a function of velocity:


title: Momentum

text: Within the domain of classical mechanics, relativistic momentum closely approximates Newtonian momentum: at low velocity, is approximately equal to , the Newtonian expression for momentum.


title: Momentum

text: In the theory of special relativity, physical quantities are expressed in terms of four-vectors that include time as a fourth coordinate along with the three space coordinates. These vectors are generally represented by capital letters, for example for position. The expression for the "four-momentum" depends on how the coordinates are expressed. Time may be given in its normal units or multiplied by the speed of light so that all the components of the four-vector have dimensions of length. If the latter scaling is used, an interval of proper time, , defined by


title: Momentum

text: is invariant under Lorentz transformations (in this expression and in what follows the metric signature has been used, different authors use different conventions). Mathematically this invariance can be ensured in one of two ways: by treating the four-vectors as Euclidean vectors and multiplying time by ; or by keeping time a real quantity and embedding the vectors in a Minkowski space. In a Minkowski space, the scalar product of two four-vectors and is defined as


title: Momentum

text: Thus, conservation of four-momentum is Lorentz-invariant and implies conservation of both mass and energy.


title: Momentum

text: The relativistic energy–momentum relationship holds even for massless particles such as photons; by setting it follows that


title: Momentum

text: In a game of relativistic "billiards", if a stationary particle is hit by a moving particle in an elastic collision, the paths formed by the two afterwards will form an acute angle. This is unlike the non-relativistic case where they travel at right angles.


title: Momentum

text: For a particle, the relationship between temporal components, , is the Planck–Einstein relation, and the relation between spatial components, , describes a de Broglie matter wave.


title: Momentum

text: Newton's laws can be difficult to apply to many kinds of motion because the motion is limited by "constraints". For example, a bead on an abacus is constrained to move along its wire and a pendulum bob is constrained to swing at a fixed distance from the pivot. Many such constraints can be incorporated by changing the normal Cartesian coordinates to a set of "generalized coordinates" that may be fewer in number. Refined mathematical methods have been developed for solving mechanics problems in generalized coordinates. They introduce a "generalized momentum", also known as the "canonical" or "conjugate momentum", that extends the concepts of both linear momentum and angular momentum. To distinguish it from generalized momentum, the product of mass and velocity is also referred to as "mechanical", "kinetic" or "kinematic momentum". The two main methods are described below.


title: Momentum

text: In Lagrangian mechanics, a Lagrangian is defined as the difference between the kinetic energy and the potential energy :


title: Momentum

text: If the generalized coordinates are represented as a vector and time differentiation is represented by a dot over the variable, then the equations of motion (known as the Lagrange or Euler–Lagrange equations) are a set of equations:


title: Momentum

text: If a coordinate is not a Cartesian coordinate, the associated generalized momentum component does not necessarily have the dimensions of linear momentum. Even if is a Cartesian coordinate, will not be the same as the mechanical momentum if the potential depends on velocity. Some sources represent the kinematic momentum by the symbol .


title: Momentum

text: In this mathematical framework, a generalized momentum is associated with the generalized coordinates. Its components are defined as


title: Momentum

text: Now if a given coordinate does not appear in the Lagrangian (although its time derivative might appear), then


title: Momentum

text: Even if the generalized coordinates are just the ordinary spatial coordinates, the conjugate momenta are not necessarily the ordinary momentum coordinates. An example is found in the section on electromagnetism.


title: Momentum

text: In Hamiltonian mechanics, the Lagrangian (a function of generalized coordinates and their derivatives) is replaced by a Hamiltonian that is a function of generalized coordinates and momentum. The Hamiltonian is defined as


title: Momentum

text: where the momentum is obtained by differentiating the Lagrangian as above. The Hamiltonian equations of motion are


title: Momentum

text: As in Lagrangian mechanics, if a generalized coordinate does not appear in the Hamiltonian, its conjugate momentum component is conserved.


title: Momentum

text: Conservation of momentum is a mathematical consequence of the homogeneity (shift symmetry) of space (position in space is the canonical conjugate quantity to momentum). That is, conservation of momentum is a consequence of the fact that the laws of physics do not depend on position; this is a special case of Noether's theorem. For systems that do not have this symmetry, it may not be possible to define conservation of momentum. Examples where conservation of momentum does not apply include curved spacetimes in general relativity or time crystals in condensed matter physics.


title: Momentum

text: In Maxwell's equations, the forces between particles are mediated by electric and magnetic fields. The electromagnetic force ("Lorentz force") on a particle with charge due to a combination of electric field and magnetic field is


title: Momentum

text: The quantity formula_60 is sometimes called the "potential momentum". It is the momentum due to the interaction of the particle with the electromagnetic fields. The name is an analogy with the potential energy formula_61, which is the energy due to the interaction of the particle with the electromagnetic fields. These quantities form a four-vector, so the analogy is consistent; besides, the concept of potential momentum is important in explaining the so-called hidden-momentum of the electromagnetic fields


title: Momentum

text: In Newtonian mechanics, the law of conservation of momentum can be derived from the law of action and reaction, which states that every force has a reciprocating equal and opposite force. Under some circumstances, moving charged particles can exert forces on each other in non-opposite directions. Nevertheless, the combined momentum of the particles and the electromagnetic field is conserved.


title: Momentum

text: The Lorentz force imparts a momentum to the particle, so by Newton's second law the particle must impart a momentum to the electromagnetic fields.


title: Momentum

text: where is the vacuum permeability and is the speed of light. The momentum density is proportional to the Poynting vector which gives the directional rate of energy transfer per unit area: