Talk:Equations of motion

message: Changed:
:\phi=\omega_0t+\tfrac12\alpha t^2\,
to:
:\phi=\phi_0+\omega_0t+\tfrac12\alpha t^2\,
to correctly account for the initial angular displacement — Preceding unsigned comment added by 173.180.188.238 (talk • contribs) 06:05, 20 November 2010 (UTC)
thread_title: Equations of circular motion

message: I wonder if it's very correct to say that \frac{\int_{t_0}^{t_1}v\,dt}{t_1-t_0}=\frac{v_1+v_0}{2}, or (u+v)/2, even if the time difference is assumed to be very small... that's probably why I never have encountered those equations, at school or at the university... Might be useful though for physics programming, for example.  —The preceding unsigned comment was added by 82.181.203.54 (talk) 12:01, August 21, 2007 (UTC) 
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Can anyone remember how those 4 equations are derived (presumably, from Newton's Laws)? -- Tarquin 05:19, 30 July 2002‎ (UTC)
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Hey, maybe It's different in Australia (though I cannot understand why), but I have always been taught that displacement is represented by x, and s represents speed (as distinct from velocity, speed is distance traveled over time, velocity is displacement over time and is a vector)
Just a thought. — Preceding unsigned comment added by 202.45.119.135 (talk • contribs) 22:58, 19 November 2007 (UTC)
thread_title:  Equation 2 

message: Is anyone else bothered by the fact that at least 3 different notations are used in this article, e.g. d = distance = s; initialocity = u = v0 = vi; etc. etc.
Also, why 'current'? These equations work perfectly well if the 'final velocity' is not current.   Ian Cairns 16:48, 13 Oct 2004 (UTC)
replies: text: To go from (equation 2) average v = s/t to (motion equation 2) s = 1/2 * (u + v) * t, you need to remember that under a constant acceleration, the average velocity is half the final velocity. — Preceding unsigned comment added by 63.161.169.65 (talk • contribs) 19:32, 29 March 2005 (UTC)

text: If we're being picky, d represents distance (a scalar) while s represents displacement (a vector). It does bother me, but they're all easily derived using mental logic. ThomasWinwood 19:07, May 11, 2005 (UTC)
Thinking it may be worthwhile changing everything into SUVAT, and adding a note at the start that Vf=V, Vi=U, etc. Basically, mentioning that there's other notations used, but in this article, the notion used will be SUVAT. Anyone agrees? -Aldo  — Preceding unsigned comment added by 2001:1388:803:9D53:E0C6:BB2B:E975:4285 (talk) 21:54, 26 September 2014 (UTC)
thread_title: Notation

message: Torricelli's Equation
Should this be merged and redirected?Atomiktoaster 00:32, 10 Jun 2005 (UTC)
thread_title: Torricelli's Equation

message: My science teacher told me that they changed the pronumeral for displacement from "s" to "R". Is this OK?
The Updater would like to talk to you! 07:48, 22 March 2007 (UTC)
thread_title:  Displacement question 

message: Why is this article called "Equation of motion" when it is clearly about more than a single equation? Even the opening sentence says "equations of motion". --Dr Greg (talk) 13:15, 4 March 2008 (UTC)
thread_title:  Only one equation? 

message: The correct equations are given with proper derivation at User:Narendra_Sisodiya/mechanics
Equation give on the page are not correct as 
* they do not maintain notion of function in S(t)
* the initial location and time was assumed to be zero,zero , why to give subset of equations
* they do not have vector associated with them, without a vector a velocity becomes speed.  —Preceding unsigned comment added by Narendra Sisodiya (talk • contribs) 21:58, 17 July 2008 (UTC)
replies: text: The reasons above do not make the equations incorrect. They are just less complete than they could be. See my reply to your question on my talk page. --Dr Greg (talk) 16:26, 18 July 2008 (UTC)
thread_title:  Correct Equation of motion 

message: I notice an IP's inconsistently replaced "s" with "x" in some of the equations and descriptions. I'm reverting that. My reasoning is:
* "s" is by far the most common form.
* An encyclopaedia is meant to be current, not a historical re-enactment. A note of the historical use of x is sufficient.
* It's inconsistent with other use on this page (the change was not complete).
* It's inconsistent with other use elsewhere in the encyclopaedia (eg the Norse, Dutch, etc versions of this page).  —Preceding unsigned comment added by DewiMorgan (talk • contribs) 07:12, 12 March 2010 (UTC)
thread_title:  Classic version? 

message: Some equations for the motion of charged particles shold be inserted.--86.126.25.12 (talk) 18:33, 29 August 2011 (UTC)
thread_title:  Motion of charged particles 

message: I think the current definition of "Equations of motion": "Equations of motion are equations that describe the behavior of a system as a function of time.", is too broad, too vague. The heat equation describes the behavior of a system in which heat flow occurs as a function of time, but it isn't an equation of motion. I don't have an alternative formulation at this point, just wanted to see if people would agree with me. /Andreas — Preceding unsigned comment added by Andreasdr (talk • contribs) 09:39, 6 October 2011 (UTC)
thread_title:  Definition too broad 

message: The derivations should be updated as they are too brief and need to be more intuitive, the derivations on the [Velocity] page (in the equations of motion section) are much better and easier to follow. "Shine on you crazy diamond" (talk) 14:33, 11 December 2011 (UTC)
thread_title:  Derivations 

message: This article appears to present the equations of motion of a single body in a uniform gravitational field, or perhaps in no gravitational field at all. Yet the title does not imply such a limitation. I see no equations that describe the motions of two bodies in mutual gravitational attraction, and no discussion of the difficulty (perhaps the impossibility) of constructing closed-form equations for systems containing three or more bodies (the Three-body problem). Something needs changing. David Spector (talk) 20:54, 29 December 2011 (UTC)
thread_title:  Only one body? 

message: Given Hamilton's equations:
:\dot{p}_i = -\frac{\partial H}{\partial q_i} \quad \dot{q}_i = + \frac{\partial H}{\partial p_i} 
then Maschen correctly wrote that if you take each equation, switch pi for qi, and H for −H, the equations are the same:
:\dot{p}_i = -\frac{\partial H}{\partial q_i} \quad \xrightarrow[]{p_i \rightleftharpoons q_i,\, H\rightarrow -H} \quad \dot{q}_i = -\frac{\partial (-H)}{\partial p_i} \quad\rightarrow\quad \dot{q}_i = +\frac{\partial H}{\partial p_i} 
:\dot{q}_i = +\frac{\partial H}{\partial p_i} \quad\xrightarrow[]{p_i \rightleftharpoons q_i,\, H\rightarrow -H} \quad\dot{p}_i = +\frac{\partial (-H)}{\partial q_i} \quad\rightarrow \quad \dot{p}_i = -\frac{\partial H}{\partial q_i}
So its not about the antisymmetry of only interchanging pi and qi, he wrote about simaltaneously switching H for −H also. F = q(E+v×B) ⇄ ∑ici 07:29, 31 March 2012 (UTC)
replies: text: I will tweak this bit, it reads better to consider the antisymmetry between H for −H since this is just one change, rather than the additional change between p and q.  Maschen (talk) 14:16, 15 August 2012 (UTC)

text: Nevermind - if you change one pair you change the other, seems fine as it is... Maschen (talk) 14:21, 15 August 2012 (UTC)
thread_title: Hamiltonian symmetry or anti-symmetry?

message: Some equations (kinematic and dynamic) concerning the motions on spirals should be added.--188.26.22.131 (talk) 14:57, 14 August 2012 (UTC)
replies: text: There already are. Spiral motion is just a combination of radial and angular motion. These equations describe radial and angular motion, and have their special cases summarized in the table following them. There is also the 3d generalization for rotational motion in space. There is also Newton's 2nd law for rotation, which would predict any form of rotational motion (obviously classically). Maschen (talk) 08:00, 15 August 2012 (UTC)
thread_title:  Motion on spirals 

message: Is this necessary? 
The section Equations of motion (Quantitative) first mentions the position and momentum vectors, then gives a detailed description in section Equations of motion (Position vector) of the position vector in various coordinate systems. This should be in the main article Position vector. 
Same for the generalized coordinates in the section Equations of motion (Generalized coordinates). Much of this could be moved to Analytical mechanics (D'Alembert's principle, generalized coordinates and constraints), because it’s a brief general description, rather than the main article generalized coordinates since links direct to there.
I intend to make these changes now. Maschen (talk) 10:47, 15 August 2012 (UTC)
replies: text: Done. Maschen (talk) 13:32, 15 August 2012 (UTC)
thread_title:  Plentiful emphasis on position vector and generalized coordinates? 

message: I have tried my best to cover the arrival of a primitive form of SUVAT equation. But I have to dig deep within literature to find out the beginning of the usage of the modern SUVAT formulae. Reading, reading, ... Bkpsusmitaa (talk) 07:07, 19 August 2015 (UTC)
replies: text: Looks OK but a lot seems to be on the history of science and mathematics in general. Put the context into the development of dynamics and equations of motion. M∧Ŝc2ħεИτlk 12:57, 20 August 2015 (UTC)
replies: text:  I have only just begun ;-) The context is curiosity (how everything around me works) and distrust (how scriptures totally fail to explain the physical world), and intent to address the curiosity and distrust. I will do it over a period of time. Patience, patience ... I have not found any history of physics/mathematics book talking about Suvat. Rest history, just like the back of my hand ... Bkpsusmitaa (talk) 03:35, 21 August 2015 (UTC)
thread_title:  The arrival of a primitive SUVAT equation addressed 

message: I beleive you have a sign wrong in your Hamiltonian (electrodynamics), It is supposed to be :
: H = \frac{\left(\mathbf{P} - q \mathbf{A}\right)^2}{2m} + q\phi \,\!  
since 
: H = \mathbf{P} \cdot \mathbf{r}- L 
It would probably be useful to mention that for simple systems the Lagrangian is the kinetic energy MINUS the potential energy and the Hamiltonian the kinetic energy PLUS the potential energy. Also the so called ACTION integral earlier in the article is a path integral, over the path that make the action stationary, OR I think just don't go into these details.  
Regarding the other parts of the article, may I suggest to make it clear that r in Cartesian coordinates is r = (x,y,z) and show how the equations then get split up in one per coordinate. Everybody seems to think that it is obvious that there are no interaction between coordinates and of course the vector nature of the equations indicate that but, it is a kind of miracle that it is true so should be pointed out. 
SUVAT must be some kind of American thing. Never heard about it, and things like that does not seem to encourage any kind of thinking. 
To be honest I liked your article a lot for its good historical introduction and the initial equations, but less and less reading along.
Too much to be a simple introductory article.
[[Burningbrand (talk) 09:56, 30 August 2015 (UTC)
replies: text: Yes, typo, whatever. (I don't remember adding the equation, and have not concentrated on the section so didn't notice). Still rewriting the article as it is. The "suvat" name is mostly used at school or very early undergrad level. I intend to rewrite the section to be more encyclopedic, since the algebra is so trivial anyone should be able to derive the equations with a little guidance. I we could mention the the explicit expressions for the Lagrangian (T-V) and Hamiltonian (T+V) but these cases are fairly restrictive, better to just give the general functional form. Thanks for feedback anyway. M∧Ŝc2ħεИτlk 10:29, 30 August 2015 (UTC)
thread_title: Electrodynamics

message: Substituted at 14:34, 29 April 2016 (UTC)
thread_title: Assessment comment

message: The article asserts "Galileo deduced the equation s = 1/2gt2 in his work geometrically,[4] using the Merton rule, now known as a special case of one of the equations of kinematics". This is simply not true. Nowhere in Galileo's work can one find something like that. Galileo's true law of free fall reads v ~ t, thsat is, v:t = constant. Generally Galileo does not use equations (structure A = A) but geometric proportions (structure A:B = C:D = k = constant). Ed Dellian. 2003:D2:9722:6B80:18F3:7E61:E1C9:E584 (talk) 12:30, 29 September 2020 (UTC)
thread_title:  Did Galileo develop the equation s = 1/2gt2?