Talk:Virtual work

Virtual force
Will someone please crack a textbook and find a good definition for virtual force and place it at the top of the article, as I have done for virtual displacement? Thanks. ChrisChiasson 05:42, 24 September 2007 (UTC)

The article mentions that virtual force can refer to a force or a moment. Can someone explain how moments are used in the basic equations? (I don't see moments mentioned anywhere else...) 141.83.42.10 (talk) 05:45, 8 July 2011 (UTC) Ok, understood my problem: If there are external moments, they can simply replace the product of force and its infinitesimal displacement. Is this correct? Can this be mentioned somewhere? Thanks. — Preceding unsigned comment added by 141.83.42.10 (talk) 06:08, 8 July 2011 (UTC)

Lagrangian Mechanics
Virtual work doesn't just provide a method of obtaining deflections in continuum mechanics. It also forms the basis of Lagrangian mechanics - a point which seems to have escaped (most of) that article. I intend to write some stuff about that aspect of virtual work here so that I may refer to it from there. Hopefully, this will be an opportunity to make the virtual work article more well rounded. ChrisChiasson 05:42, 24 September 2007 (UTC)

Use of the term "Imaginary"
In certain cases, it is not clear if the original author(s) intended to use the term "imaginary" for terms being expressed as complex numbers, or if those terms are to be thought of as non-physical, i.e. virtual or "make-believe" as we would suspect. There are conjugates for virtul work in the complex plane (sorry, no reference). I suspect that because the formulation of virtual displacements and work is related to a differential formulation of equilibrium, and because the differential operator of the differential form is usually positive-definite, that complex numbers may not be not expressible by the principle of virtual work/displacements. In other words, the principle of virtual work/displacement is applicable for real (i.e. not complex numbers) numbers. Please consider revising. - URjyoung 15:54, 28 September 2006 (UTC)


 * Thanks for pointing out the need for clarification. Revised version now defines "real" as being "actual" while "imaginary" as "fictitious". TVBZ28 14:59, 30 September 2006 (UTC)

Rotations and Translations
This needs something about rotational vs. translational systems, and how you can treat the virtual work along rotations and translations as seperate.


 * Translations and rotations need not be treated separately, if both are required. We use what we need for the particular system and objective. For example, for particles and truss systems, there is no need for virtual rotations. On the other hand, for rigid bodies and frames, both translations and rotations are often needed, but again, that depends on what we want. Admittedly, virtual work principle is an abstract concept that even text-book authors confuse it with the principle of conservation of energy. After all, virtual displacements (rotations) are arbitrary: you choose to impose what you want, as long as it's consistent with the nature of the system. One part of the difficulty is that those who really understand it often expound it in complex mathematical terms. The second part is that the applications are so wide that a beginner might have experienced only a few situations, similar to a blind man who thinks of an elephant as a big worm while touching the elephant's trunk. The worst part is that many things are arbitrary, and most people don't know what they want, or how to get what they want. The fact that virtual displacements\forces are arbitrary is precisely the reason why virtual work principle is so powerful, unlike the principle of conservation of energy, which is nearly useless in structural mechanics. I'd hope though that most readers will be able to grasp all the nuances of the article after some pretty serious thinking and practice with the examples and exercises in the references.TVBZ28 19:43, 3 January 2006 (UTC)

Virtual?
Nowhere in the article is the term "virtual" defined. It just describes multiplying random Ds by the forces and then says those Ds are "virtual displacements". Overall, the article seems like a circular definition. &mdash;BenFrantzDale 19:51, 28 September 2005 (UTC)


 * That seems to be a valid criticism. The article relies on prior knowledge of calculus, particularly the differential.  Since the work done is infinitesimal, it can only be defined in terms of other infinitessimals, but the concept of a differential should be introduced or at least linked to in a more accessible way if you were confused.--Joel 02:36, 29 September 2005 (UTC)

A defintion of "virtual" has been introduced. Virtual work is also valid for finite displacements and rotations (even though in applications, small displacements & rotations are often used). In any case, little is gained by introducing the more rigorous concept of "variations" at this stage. &mdash;TVBZ28 23:45, 14 December 2005

Rewrite
I'm considering doing a rewrite, but first I want to make sure I understand things. It seems that finding equilibrium using virtual work is just a special name for finding equilibrium by setting the variation of the energy of the system. Another way of saying this, I think, is that in as much as forces "want" to cause displacements, if you can find a configuration for which any small variation from that configuration results in no net work being done by the forces, you have found a configuration that is stable. Does this sound right? Does this sound like a starting point for a clearer article? —BenFrantzDale 04:47, 1 December 2005 (UTC)
 * OK, I rewrote it. Please fix it furhter if it needs fixing. —BenFrantzDale 05:28, 5 December 2005 (UTC)

One of the applications of the virtual work principle is to find the equilibrium configuration, and in such case, it is more apt to call it the principle of virtual displacements. On the other hand, the principle of virtual forces will lead to compatbility equations.

Since the objective of the article is to introduce the concept of virtual work, it should be kept simple as is. More in-depth treatment of the two principles and their applications as well as of variational principles and calculus can be dealt with, if desired, in additional articles. —TVBZ28 24:00, 14 December 2005


 * Keeping it simple is all well and good but, while I think I understand virtual work (at least as I described it in a previous version of the article), I do not understand the current version; I get lost at the first sentence: "Virtual work is the mathematical product of unrelated forces and displacements or of moments and rotations." When I read that I think "Ok, so if I multiply the weight of Chewbacca on Endor by the distance from the earth to the sun, that must be virtual work", which makes no sense. While I can basically see that the current article says what virtual work is, it doesn't answer for why it is useful or how it came about. That is what I was trying to accomplish in my rewrite. &mdash;BenFrantzDale 16:37, 15 December 2005 (UTC)


 * That is correct as long as the "weight of Chewbacca on Endor" and "the distance from the earth to the sun" are in the same direction; however, (i) what is the use of such virtual work is another matter; (ii) the use of large displacements will cause complications in the case of deformable bodies. We should not mix up the general definition and the usual applications. The main point is that the forces and/or the displacements could be arbitrary but in the same direction--otherwise the product is not work. —TVBZ28 18:46, 15 December 2005
 * Actually, I suppose as long as we use a dot product, direction shouldn't matter. But still, in the current version I don't see an explanation of what virtual work means, why this approach is useful, or how it comes about. As I understand it, virtual displacements only make sense when they are infinitessmal&mdash;that is, when you take the variation of the position of the system. In that context, its utility is that the configuration with zero virtual work is the stable configuration, and physically that configuration means "if the configuration were to change a little bit, no forces would 'get to' do any work; since no forces would get to do any work, they won't do work so the configuration won't change." In short, I would like to see the article address the questions of what it means, why it is useful, and how it is used; at the moment I only see an answer to "what it is" and one which at least I didn't find very approachable. &mdash;BenFrantzDale 00:24, 16 December 2005 (UTC)

- Agreed that if we use dot product, then direction shouldn't matter, but that needs more pre-requisite knowledge. - Virtual displacements could be finite, and in the case of a single particle where compatibility of displacements is a non-issue, they are completely arbitrary as shown in Eq.(b). Obviously finite displacements (& rotations) cause lot of complications including the need to use different kind of stress tensors. - The example on the particle shows:
 * What is virtual work: Eq.(b) & (c) define virtual work.
 * Application: Eq.(c) leading back to (a) shows how virtual work can be used for imposing equilibrium. This application should show the motivation.

Obviously, such demonstration is a bit more complex for the case of deformable bodies, and serious readers should refer to more specialized books or reference material. — TVBZ28 00:59, 16 December 2005 (UTC)

If you want an idea of how the article should be written with clarity, take a look at:-

http://ocw.mit.edu/courses/aeronautics-and-astronautics/16-61-aerospace-dynamics-spring-2003/lecture-notes/lecture9.pdf

212.139.80.204 18:47, 22 April 2007 (UTC)
 * Actually there are two way of introducing the virtual work principle. The first one, which is the historitical point of view is what was stated by Bernoulli in "Nouvelle mécanique de Varignon 1725" and also close to the currently known as "D'Alembert principle" and is somehow very close to the current form of the article (speaking about perturbing the equilibrium, that can be a dynamical equilibrium etc...). As far as I'm conerned, that way of introducing theses concepts is rather unclear to me, because the only text I am able to find are in old language and the terminology has change so much. The other way of introducing that principle is a much more mathematical way of thinking wich lead to what we call "principle of virtual powers". Bascily that principle is a dualised version of Newton second law (F=ma) and of the reciprocal actions (F1->2 + F2->1 = 0). Meaning that if you dot produce these laws by an arbitrary motion field (virtual motion) then you got the virtual power balance : $$\mathcal{P}_a=\mathcal{P}_i+\mathcal{P}_e$$ and that if you take as virtual motion a rigid body motion, then $$\mathcal{P}_i=0$$. These two things are the two equations of the VPP and are équivalent to Newton's law and allow to deal with allmost every mecanical problem. If some of you have some knowledge in French, you can try reading principe des puissances virtuelles, that is a draft of article about VPP I wrote.
 * Drébon (talk) 12:23, 15 July 2008 (UTC)
 * Drébon (talk) 12:23, 15 July 2008 (UTC)

What is the use of this principle?
What is the use of the principle of virtual work? Does it allow you to solve problems you couldn't solve with a force diagram? Does it make solutions simpler? I think the article would benefit from an example of how and why this principle is used. 128.135.230.129 (talk) 20:32, 1 October 2009 (UTC)


 * iski vyakhya bhi kare 2402:8100:2751:EBF8:3712:FA62:182D:87C0 (talk) 15:28, 29 June 2023 (UTC)

Principle of virtual displacements
"I have a opinion that the results from a displacment method and a force method would be different depending shape functions used in the displacement method and it would be helpful to adress this issue to the reader's of this topic." Changhee1220 (talk) 12:39, 30 April 2011 (UTC)

Revisions to this article
I would like to propose some revisions to this article. In its most basic form the principle of virtual work is critical to the analysis of machines modeled as assemblies of rigid bodies. Separately, this principle finds use in the study of deformable bodies. These are two very important but different areas in mechanics. Can we provide a general introduction and then separate the presentation of these topics to help the reader? Prof McCarthy (talk) 06:13, 7 July 2011 (UTC)

The current version of this article addresses much space to deformable bodies. I will focus my efforts on the classical formulation of virtual work for rigid body systems. You can see what I am developing at the Virtual work draft. I would appreciate any advice. Prof McCarthy (talk) 20:11, 8 July 2011 (UTC)

I added the new introduction, and commented out the old one. I thought it became too technical too fast, but anything that is considered important can be added by just selecting it from the commented section. Prof McCarthy (talk) 21:21, 8 July 2011 (UTC)

I added a small section on the history of virtual work. Prof McCarthy (talk) 17:27, 9 July 2011 (UTC)

I added the introduction section that I hope provides useful definitions of the basic concepts of the principle of virtual work. Prof McCarthy (talk) 01:40, 10 July 2011 (UTC)

I expanded the section on static equilibrium. I commented out some of what was there before. I hope that is ok. I am close to being done. I would like to add a couple examples. Prof McCarthy (talk) 03:19, 11 July 2011 (UTC)

Sample figure of virtual displacement
I am thinking about adding the figure shown at right to the article. Hopefully this will be of some help in explaining the concept. Please comment. Thanks!--LaoChen (talk)05:46, 13 July 2011 (UTC)


 * This is a good contribution. This figure would be very helpful.  I would only ask that perhaps points be added to distinguish the start and the end, so the dashed line at the end is separated from the solid line.  Thank you,  Prof McCarthy (talk) 13:29, 13 July 2011 (UTC)


 * I have made a new figure. If this figure is OK, please let me know where I can place it.  Thanks!--LaoChen (talk) 04:40, 14 July 2011 (UTC)
 * Looks great! Prof McCarthy (talk) 06:41, 14 July 2011 (UTC)
 * On second thought, this figure may not be appropriate for the article. So, I would like to pull it out from this article.--LaoChen (talk)02:54, 24 July 2011 (UTC)

One degree of freedom mechanisms
I added a section on the use of virtual work in the static analysis of one degree-of-freedom mechanisms. I hope to add examples in the near future. Prof McCarthy (talk) 06:17, 20 July 2011 (UTC)

I have added a detailed derivation of the law of the lever using the principle of virtual work. It is probably over-done, but I believe it illustrates the calculations and the insight that they can provide. Prof McCarthy (talk) 15:24, 21 July 2011 (UTC)

I have added the virtual work analysis of a gear train, which is rather straight forward. Prof McCarthy (talk) 03:12, 22 July 2011 (UTC)

Generalize forces are zero? Or sum of them is zero?
This seems incorrect to me: "The principle of virtual work requires that a system of rigid bodies acted on by the forces and moments Fj and Mj is in equilibrium if the generalized forces Fi are zero."

Since you can define your generalize coordinates such that the generalized forces are exactly equal to the real forces, how could this possibly be true? You can easily construct a trivial system in equilibrium such that the generalized forces are not zero. Or am I misunderstanding something?

On the other hand, the sum of all the virtual work done by each generalized force is zero in a system at equilibrium. Perhaps this is a misstatement of this? PenguiN42 (talk) 00:57, 5 November 2011 (UTC)


 * I understand your question, and I believe the source of the confusion is the statement "since you can define your generalize coordinates such that generalized forces are exactly equal to real forces." The definition of generalized forces yields one generalized force for each generalized coordinate, or degree of freedom, of the rigid body system.  This means a four-bar linkage with forces applied at the input and output has a single generalized force.  Individual generalized forces are coefficients of variations of independent generalized coordinates in a differential that must be zero.  I hope this helps. Prof McCarthy (talk) 16:36, 6 November 2011 (UTC)

virtual work done by moments (torques)
I find the equation about the virtual work done by an applied moment misleading, since it suggests that you have to differentiate the rotation vector towards the generalized coordinates (calculate a jacobian), but that is not true. Every time I need to apply a moment I come across this topic and I'm struggling with it but it does not need to be so difficult. Therefore i would like to add something in plain English on how to calculate the virtual work done by a moment. If w is a (3x1)unit vector pointing in the direction of the moment M, seen in an absolute coordinate system and r is the (3x1)unit vector pointing in the direction of generalized coordinate i, also seen in an absolute coordinate system, then the virtual work Q done by M in the direction of qi is

Q(i) = w.'*r*T,

Where T is the norm of M. That said I hope i will never be confused again. — Preceding unsigned comment added by Street missile (talk • contribs) 11:18, 23 November 2011 (UTC)


 * I am certain that this article can always be improved, however, I believe the easiest way to compute the generalized force associated with a moment is to compute the dot product of the moment with the partial rate of change of the angular velocity vector with respect to the time derivative of a particular generalized coordinate. This is a rather simple operation, though difficult to describe.  I am fairly certain that the dot product of the moment vector with a position vector is not the correct calculation. Prof McCarthy (talk) 00:54, 24 November 2011 (UTC)


 * With the dot product, I do not mean the dot product with a certain position vector pointing to a certain location. In my example, r is a vector oriented in the direction of a generalized coordinate. I'm not sure if the mathematic symantics of my writing is correct, but it sure is the way to implement it. off course, care must be taken which coordinates are affected by the Moment. For example, a moment never does virtual work on a translational coordinate. So in that respect, it is true that you cannot blindly take all position vectors and multiply them with the moment. Thanks for the reply.--Street missile (talk) 09:10, 24 November 2011 (UTC)

The outcome is selected...
An editor has revised the sentence "that nature selects from from a set of "tentative" realities.." to "the outcome is selected from a set of "tentative" realities." I guess the passive voice eliminates the need to think about who or what is doing the selecting, but the fact remains that the theory is clear that of the many trajectories the one that we experience is the one that optimizes a quantity. While the personalization of this as "selection" may bother some today, it was the culture of the time to consider this indeed to be a selection. We can acknowledge this though it may not match our current understanding. Then again it is worth noting that modern physics and cosmology are ambiguous on this issue of our selection among possible universes. Prof McCarthy (talk) 02:33, 12 May 2012 (UTC)
 * As long as a the verb "select" is used, I think the change makes no principal difference, the "active" idea being present in the verb itself. In my opinion, more neutrality might be achieved by introducing formulations like "takes place" or "occurs". At the same time, I have not read the Aristotle works cited in the next sentence but if the "selection" wording is close to his reasoning, it might be all right tn the History section... --Dontknowhow (talk) 03:52, 12 May 2012 (UTC)

Figures?
Where are the figures cited for the deformable bodies section? — Preceding unsigned comment added by 2620:83:8001:24:0:0:1:174D (talk) 18:29, 10 January 2017 (UTC)