Talk:D'Alembert's principle

message: What is ri in the first equation?
ri are the components of position vector of the ith particle of the system.  —Preceding unsigned comment added by 117.200.61.215 (talk) 13:39, 4 October 2009 (UTC)
thread_title:  First equation 

message: The name of this person is written as d'Alembert in this article. Can anyone please confirm if this the appropriate way to write the name. I have seen several text books where the capital D is used. Ref : A first course in continuum mechanics Y.C.Fung . Pjacobi could you please take a look at Ch.1 page 8 Mathematical Formulation of Physical Problems in the book mentioned earlier. I believe you are stating correct.
 —Preceding unsigned comment added by 129.240.21.182 (talk) 13:30, 3 September 2007 (UTC)
replies: text: In Goldstein's book "Classical Mechanics", the person's name is D'Alembert, and the principle is called D'Alembert's Principle.  However, in Beer & Johnston's book "Vector Mechanics for Engineers", the name is d'Alembert.  I guess, to make sure the usage is correct, you need to consult with a French specialist. Thurth 05:34, 1 October 2007 (UTC)
replies: text: Is there some kind of process that can be requested for this?ChrisChiasson 15:03, 2 October 2007 (UTC)
thread_title:  name 

message: This article was automatically assessed because at least one WikiProject had rated the article as stub, and the rating on other projects was brought up to Stub class. BetacommandBot 09:47, 10 November 2007 (UTC)
thread_title:  WikiProject class rating

message: Having been derived from Newton's second law, D'Alembert's principle is a refinement of Newton's second law.  How can it be equivalent to Newton's second law?--Thurth 04:13, 17 November 2007 (UTC)
replies: text: I'm not sure the form of the principle stated in the article there is conform, but if you take it as the principle of virtual power (see my above remark or http://fr.wikipedia.org/wiki/Principe_des_puissances_virtuelles) you can derive Newton's law and much more from that principle Drébon (talk) 18:00, 13 July 2008 (UTC)
replies: text:  Sorry guys, but its just wrong to state, that D'Alembert's principle is equivalent to Newtons Second Law. This misses important simplifications, such that the sum of the virtual work, vanishes. Snake707 -- de.Wikipedia --87.145.69.208 (talk) 21:00, 3 June 2010 (UTC)
replies: text:  Usually the virtual displacements in d'Alemberts principle (F-ma)\delta r=0 are along constrained lines. However, for an unconstrained (=free) particle, there are no restrictions on the \delta r. For the equation to be valid for all \delta r, the equation F-ma=0 must hold, which is just Newton's second law. I would not really call this an "equivalence" but sure the two are related. --Dogbert66 (talk) 15:28, 14 April 2012 (UTC)

text: Well, d'Alembert's principle of virtual work is equivalent to Newton's laws, as can be seen from the fact that they both lead to the exact same equations of motion. In fact, one learns in a course on advanced classical mechanics that d'Alembert's principle leads to (a version of) the Euler-Lagrange equations. Nerd271 (talk) 03:29, 24 June 2020 (UTC)
thread_title: Equivalence between D'Alembert's priciple and Newton's 2nd Law

message: Hello,
my textbooks says, that the principle of D'Alembert can only be derived in very easy cases e.g. a mass particle, or a rigid body.  The problem in deriving the principle for not rigidly bound masses is the anistropy of the configuration space.  The problem can be "solved" by approximation with rational masses.
Source: Eckhard Rebhan: Theoretische Physik: Mechanik, section 5.4. "Exkurs: Ableitung des D'Alembertsche Prinzips"
mfg  —Preceding unsigned comment added by 87.145.74.41 (talk) 20:26, 13 March 2010 (UTC)
thread_title:  Danger ... Derivation 

message: The introduction states
:D'Alembert's contribution was to demonstrate that in the totality of a dynamic 
:system the forces of constraint vanish. That is to say that the generalized forces :{\mathbf Q}_{j} need not include constraint forces.
Can someone provide (a link to) this demonstration? If the forces of constraint vanish in the totality of the dynamic system, one could express this as  \mathbf{C}_i = 0  and enter this in the section Derivation_for_special_cases.
82.92.241.131 (talk) 07:03, 8 September 2010 (UTC)
thread_title:  Vanishing forces of constraint 

message: My professor (who will rename nameless, but is a venerable scholar in physics) said that Newton already derived this principle, and was referred to as his "4th law". (more specifically, he claimed that Newton lumped what are usually called the 2nd and 3rd law together, and this was the orginal 3rd law, and later became a "4th").  This makes sense since it is an additional principle for dealing with constraints, therefore it must be considered a fundamental law (or axiom) in Newtonian mechanics. He said he read about this in a book by Lord Kelvin, and that later authors brushed it aside as being "not as fundamental" as the other 3 laws. I did a quick search and couldn't find any information, but I figured I'd mention it. Perhaps someone could look into this. Danski14(talk) 20:39, 8 September 2010 (UTC)
thread_title: History

message: D'Alembert's principle of virtual displacements opens a way to find orbits of mechanical systems under constraint qualifications. If there are no constraints then it says only that the zero vector is the only vector perpendicular to all other vectors. Suppose that the original mechanical systems has n degrees of freedom and that there are m < n functionally independent holonomic-scleronomic constraints in implicit form, then these constraints have in every point m linear independent normals and n - m linear independent tangents which are perpendicular to the normals. These tangents are the virtual displacements of the principle. The vector of Newtons equations of motion must be perpendicular to all tangents. In Lagrange's multiplier method, this vector must be a linear combination of the normals (constraint forces) and the factors of the linear combination are the multipliers. In the first case, we obtain a system of n-m differential equations and m "algebraic" eqations (the constraints) for n variables, and a system of n differential equations and m "algebraic" equations for n+m variables in the second case. Therefore, the result is a differential-algebraic system in any case. Both methods are dual to each other in geometrical sense by a simple result on the range of a matrix. --E.W.Gekeler (talk) 17:16, 17 June 2013 (UTC)
replies: text: In my opinion this analysis is correct, and shows that the following statement is wrong: "To date nobody has shown that D'Alembert's principle is equivalent to Newton's Second Law. This is true only for some very special cases e.g. rigid body constraints. However, an approximate solution to this problem does exist."Prof McCarthy (talk) 23:40, 6 July 2013 (UTC)
thread_title:  Geometry 

message: Substituted at 12:39, 29 April 2016 (UTC)
thread_title: Assessment comment

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thread_title:  External links modified 

message: "D'Alembert's principle is a more general case . And it is true only for some very special cases..."
General, but only works for special cases. I think this could be expressed in a less confusing way. --Inc (talk) 21:12, 18 March 2019 (UTC)
thread_title:  General or special? 

message: The statement of the principle in the beginning is unclear and confusing in several ways. First, the equation after the statement is different from what the statement claims it to be: the momenta and the constraints of the system which are in the text are missing in the equation. Second, inertial forces, the essence of d'Alembert's principle, are missing altogether. Third, the statement speaks about projection, which is a geometrical term. There is a whole discipline Projective Geometry. Here, nobody can tell how momenta are projected on virtual displacements. Fourth, virtual displacements require much explanation and sending the reader to Virtual displacement with heavy analytical mechanics most of which doesn't have anything in common with d'Alembert's principle is a big distraction and obstacle to understand the principle itself. If virtual displacement is needed in further discussion it should be explained briefly and in relation to the topic.
I'll wait for some time for someone to convince me that this text can stay as it is, and then shall replace it with a clearer and more exact statement. Lantonov (talk) 13:18, 31 October 2020 (UTC)
thread_title:  Confusing formulation of the principle

message: We sometimes encounter a formulation of d'Alembert principle that uses the Lagrangian. Instead of writing
\sum_i ( \mathbf F_i - m_i \dot\mathbf{v}_i - \dot{m}_i\mathbf{v}_i)\cdot \delta \mathbf r_i = 0,
it is written as Hamilton's principle, but for virtual changes \delta \mathbf r_i  of the i-th particle that are consistent with the constraints. 
It is more general than the form used above. Is it a form that was also proposed by d'Alembert or is it a misnomer? Discussion is welcome.
AntonyKers (talk) 14:29, 2 March 2023 (UTC)
thread_title:  Using the Lagrangian?