Talk:Rigid body dynamics

Untitled
TODO: $k$ versus $\vec{k}$ : pick one.

— Preceding unsigned comment added by 141.135.40.221 (talk) 14:01, 17 December 2017 (UTC)

Should there be some mention of moment of inertia on this page? I'm not sure if a moment of inertia is a less general thing than the matrix of moments appearing here. Even so, it might be worth mentioning. -- WillWare 02:42, 22 September 2006 (UTC)

This page needs a lot of work.

... As a non-expert but a reasonably smart guy with a basic understanding of calculus, I couldn't make heads or tails of this. When an expert does rewrite this page, please include a couple of paragraphs for the rest of us! Glancing at the kinematics page, it looks much more like an encyclopedia should. Thanks! 69.180.230.102 (talk) 18:44, 16 February 2008 (UTC)
 * It doesn't say what rigid body dynamics is, it says what it is not.
 * Rigidity implies non-deformation
 * Instantaneous change of velocity upon impact
 * Therefore no real bodies are rigid
 * RBD is a mathematical idealization of electrostatic forces e.g. when steel balls collide, though real collisions take time and cause tiny deformation
 * Painleve problem/static indeterminancy with friction
 * Resting contact -> linear complementarity problem
 * Methods of solution: impulse-based, constraint-based, projection methods
 * Rigid-body interactions (collision, joints), constraint manifold
 * holonomic/non-holonomic constraints, principle of virtual work

This article is very basically incorrect
This article mixes kinetics with kinematics. See Goldstein: Classical Mechanics. Brews ohare (talk) 23:20, 2 May 2008 (UTC)

I'm currently taking a particle rigid body dynamics course, and as the professor introduces new concepts, he starts with kinematics for the idea, then the kinetics. In other words, we are first taught to deal with describing the motion of bodies, then how to analyze what causes the motion. The most general understanding presented by the course is that kinetics and kinematics are usually inseparable topics within the concept of rigid body dynamics. 153.90.173.11 (talk) 17:13, 29 March 2010 (UTC)

Undefined, provincial notation everywhere
This page contains tons of underdefined notation and (in my opinion) provincial representations of somewhat general concepts that could be made much more accessible. I'll see if I can give this thing a go over the next few weeks. I plan to draw heavily from Kane and Levinson, whose books on dynamics present the material in a very simple and general way. MarcusMaximus (talk) 08:36, 27 August 2008 (UTC)
 * Thanks for that. If you consider yourself an expert on this topic, you may be able to help me. I'm having some problems with Newton's Bucket argument--this book I'm reading uses it as evidence for absolute motion, but I have a very simple explanation for it which doesn't require absolute motion. My idea is based on thinking of the bucket and the water as made up of particles--which of course they would be--and considering "rotation" to be just a macroscopic view of translational motion of the particles. It makes perfect sense to me, but in several centuries it seems no scientist has posed that interpretation, so I think I must be wrong in some way. I don't know how, though. And I'm not much of a mathematician. Salvar (talk) 01:53, 9 September 2008 (UTC)

Here's my attempt at it, although I haven't studied it in depth. The "group of particles" model is a valid way to view the problem. The idea of relative motion is based on the concept that any two inertial reference frames are indistinguishable. However, when the bucket it spinning, all of the particles in the bucket have a velocity tangent to a circle that each particle traces about the center of the bucket. All the particles are continuously accelerating toward the center of the bucket (I'm assuming you're familiar with centripetal acceleration). This acceleration is always perpendicular to the velocity of each particle. Therefore, in an inertial reference frame following any given particle at a given instant, that particle is accelerating. Hence, you don't need "absolute motion" to explain it. MarcusMaximus (talk) 06:09, 9 September 2008 (UTC)

Notation
What does the symbol "MbG/O" represent? I think the article should define all symbols it uses, or at least provide links to definitions. —Preceding unsigned comment added by Avl (talk • contribs) 17:09, 18 September 2008 (UTC)


 * I have no idea. I've been mulling over where to begin to fix this article, but it is overwhelming. MarcusMaximus (talk) 06:35, 19 September 2008 (UTC)

I believe M is the mass of the rigid body, and bG/0 is the vector from the analysis point (the point where you are calculating torques about) to the center of mass. —Preceding unsigned comment added by 76.216.140.213 (talk) 18:32, 25 May 2009 (UTC)

Recent changes to the lede
You are right, that large rewrites should be made off line, but it is also true, that article as I left it was readable. I needed to see what (if any) reaction I am getting. - Petr (talk) 13:14, 26 March 2010 (UTC)


 * Here is some reaction:
 * The first sentence is supposed to define the term, which should appear in bold: rigid body dynamics.
 * Wikilinks should not have underscores between the words.
 * Sentences should not be broken across separate paragraphs.
 * English grammar requires the use of many articles: definite and indefinite.
 * The colon character should be used to indent a paragraph.
 * First-person personal pronouns, such as we and us, should be avoided for being unencyclopedic.
 * Major rewrites can not remain half done. With all of these issues, the recent changes cannot remain. -AndrewDressel (talk) 21:39, 26 March 2010 (UTC)

Please review external link to Simulink model
I tried adding this external link but someone considered it spam. Would someone (preferably who is familiar with Simulink) please review it to see whether it adds value. I imagine that some readers would be interested in brief, ready-to-use models. --Tennenrishin (talk) 09:58, 11 July 2011 (UTC)
 * 6-DOF Rigid Body Dynamics - an brief overview including mathematical and Simulink Model


 * The question is not whether an external link adds value. Instead, an external link must meet these criteria, per WP:EL:
 * The question is exactly and completely whether the link improves the article, per WP:IAR. --Tennenrishin (talk) 06:35, 25 July 2011 (UTC)
 * 1. provide a unique resource beyond what the article would contain if it became a featured article.
 * The external link in question is to a page that contains a couple of diagrams and some text. These may be fantastic diagrams and wonderful text, but if that is the case, then I don't see why the article would not contain all that if it became a featured article.
 * 2. not be mainly intended to promote a website.
 * While the linked page itself does not necessarily appear promotional, the user ID used to add the link appears to be in use merely to add external links to this web site, at least in 2011.
 * 3. not be a link to a personal web pages, except those written by a recognized authority.
 * While Isak may know what he is writing about, there is no way to judge his authority on the subject based solely his first name.
 * At this time, it does not appear that links to any pages on http://www.du-preez.com would be appropriate. -AndrewDressel (talk) 10:54, 11 July 2011 (UTC)
 * 1. Simulink model.
 * The Simulink model is merely an image in png format. You are welcome to upload a copy. -AndrewDressel (talk) 15:01, 11 July 2011 (UTC)
 * Simulink is proprietary dynamic system simulation software. A Simulink model does not belong within the scope of an encyclopedic article about a topic in classical mechanics, but for some it would be a useful additional resource. That is what external links are for, no? --Tennenrishin (talk) 17:50, 11 July 2011 (UTC)
 * Perhaps. If this site truly were to become a notable resource for people interested in analyzing rigid body dynamics, then someone unassociated with it might legitimately add an external link to it. At this point, though, its insertion appears to be a conflict of interest. -AndrewDressel (talk) 08:00, 12 July 2011 (UTC)
 * 2. Assume good faith.
 * It does not alter the facts. -AndrewDressel (talk) 15:01, 11 July 2011 (UTC)
 * Adding links to a single website in a given year does not mean the intention is to promote that website. --Tennenrishin (talk) 17:50, 11 July 2011 (UTC)
 * When the only activity by a single user ID in an entire year is to insert links to a single website, then the actions of that user ID are indistinguishable from promoting that website, no matter what the intentions of the actual person might be. Since it is impossible to know the intentions of a anonymous user, we can only consider their actions. -AndrewDressel (talk) 08:00, 12 July 2011 (UTC)
 * 3. Acknowledged.
 * Oh well... I wish the link had been there when I first came to the article. --Tennenrishin (talk) 14:17, 11 July 2011 (UTC)
 * On second thoughts (if we're being technical):
 * 3. Is the definition of a personal web page one that has a title that is a common first name? --Tennenrishin (talk) 14:35, 11 July 2011 (UTC)
 * No. As the linked article states in the first sentence, a personal web page is created by an individual to contain content of a personal nature rather than on behalf of an employer or institution. -AndrewDressel (talk) 15:01, 11 July 2011 (UTC)
 * If the information on the web page is of a personal nature then Isak must be a rigid body. --Tennenrishin (talk) 16:05, 11 July 2011 (UTC)
 * Not necessarily so, as explained by paragraph 2: "Many personal pages will include information about the author's hobbies, interests..." It appears that rigid body dynamics is an interest of Isak. -AndrewDressel (talk) 08:00, 12 July 2011 (UTC)
 * I feel that we are not making good progress. We may reach consensus more economically if we concentrate on the most important matters first. Would you mind briefly summarizing your single most important objection to the link (after having absorbed our discussion above), in a way that can serve as a starting point for a new leg of the discussion? --Tennenrishin (talk) 22:42, 12 July 2011 (UTC)


 * There is no Simulink model. It's just a picture.
 * Is this your own website you're linking to? Someone else previously called you out for adding original research to the consciousness article, and best I can tell it was a link to the same website. MarcusMaximus (talk) 05:50, 13 July 2011 (UTC)
 * Yes, you are technically correct, but that feels a bit like saying a scan of an article is not an article. The picture is not much less valuable than the model, because it is easy to contruct the model if you have the picture.
 * Since you ask - yes, it is, and I have been called out for adding an OR EL. I was even less familiar with the Wikipedia guidelines then than I am now. --Tennenrishin (talk) 09:49, 13 July 2011 (UTC)
 * I am sorry, but I am not able to pick just one point as the most important. It is the combination of the three points I posted above that paints a picture of the unsuitability of this particular external link for Wikipedia. If the linked site contained a unique resource, such as the video of a compelling lecture, and the link was inserted by an editor with a recent edit history that consisted of more that simply inserting links to this site into several articles, and the author of the site identified himself as some sort of verifiable expert in the field, then there would be no need for this discussion. -AndrewDressel (talk) 06:53, 13 July 2011 (UTC)
 * I do not deny the potential for COI, and haven't up to now declared it because Wikipedia's guidelines do not require it. But I thought that for there to be a conflict of interests, there needs to be actual conflict. Can there be conflict if the link adds value to the article? That would seem more like an alignment of interests.
 * So to me the question seems to have more to do with whether the link adds value, and less to do with the activity of my ID, which is a disposable thing to a user with dishonest intentions.
 * Although I believe the link would add value, I do not assert that it does, just that there is a case to review whether it does. --Tennenrishin (talk) 09:49, 13 July 2011 (UTC)

6-DOF dynamic model
I've inserted the dynamic model from the external link discussed in previous section, into the article. Could someone review it and help with some formatting touch ups. (I don't know how to do inline Greek symbols without using the math tags, which make them bigger than they should be, inline.)--Tennenrishin (talk) 09:59, 13 July 2011 (UTC)


 * I think it's useful to have a straightforward set of equations to model 6-dof dynamics, so I commend you. Here is my review of your model:
 * What is "the 3x3 rotation matrix"? Every rotation matrix relates two vector bases (or coordinate systems), and in order to be meaningful you must specify "from" and "to".  You might as well refer to x as "the vector". --Tennenrishin (talk) 13:13, 14 July 2011 (UTC)
 * Why doesn't your formulation calculate acceleration and angular acceleration? Those are usually very important quantities.
 * All your vectors lack a reference frame.
 * I'm curious why you expressed all the rotation equations in terms of matrices instead of vectors, like the rest of the article. I suggest that you try to use the same symbols too, like N for torque. MarcusMaximus (talk) 06:55, 14 July 2011 (UTC)
 * Thank you for the feedback. Some preliminary responses for now. I hope to work it into the article later.
 * From 'world frame' to 'body frame'. I.e. the matrix rotates the object from the reference orientation of I to its current orientation.
 * The accelerations are not state variables, of course, and they are not on the 'critical path' to position/rotation, which is arguably the most important output. In my own experience acceleration is usually unimportant. If angular acceleration is really needed, there is probably no simple alternative to differentiating angular velocity.
 * 'World (i.e. absolute) coordinates' - not sure if that is what you meant.
 * The matrix representation of rotation gives this formulation of the model its simplicity, conceptually as well as for implementation in software.
 * Something else: Having used this model a couple of years back, I added it to the article thinking that it must be common-place in literature, but now I cannot find it published or used anywhere. It follows fairly straightforwardly from basic kinematic and dynamic principles, surely it can't be OR? (I'd be rather excited if it is.) Does anyone out there know? But surely... --Tennenrishin (talk) 13:13, 14 July 2011 (UTC)


 * My questions were meant to be subtle hints that in order to be useful, your description has to specify all the reference frames for every matrix and vector. I suggest using an Inertial frame and a Body frame, since these equations assume that.
 * You can calculate acceleration from a=F/m.
 * :o    Tennenrishin (talk) 16:16, 16 July 2011 (UTC) :)
 * You can get an explicit vector equation for angular acceleration by differentiating angular momentum, then solving (basically solving Euler's Equation):
 * $$\mathbf{N}=\frac{^A d}{dt}\mathbf{L}$$
 * $$\mathbf{N}=\mathbf{I}\dot{\omega}+\mathbf{\omega}\times\mathbf{L}$$
 * $$\dot{\mathbf{\omega}} = \mathbf{I}^{-1}(\mathbf{N}-\mathbf{\omega}\times\mathbf{L})$$
 * Yes, that seems like a much better approach than differentiating $$\omega$$ (if acceleration is needed). --Tennenrishin (talk) 16:16, 16 July 2011 (UTC)
 * The matrix form of the rotational dynamics has no basis in the previous parts of the article. That's why I said you should use the vector form.  Either that or add the theory to support that similarity transformation on the inertia matrix, then specify what vector basis the angular momentum and angular velocity are expressed in when you use that middle equation.
 * MarcusMaximus (talk) 04:52, 15 July 2011 (UTC)
 * Hmm, thanks. To be honest, I have trouble wrapping my head around the previous parts of the article, and don't have the motivation right now to try harder. The model, on the other hand, follows rather straightly from visualizations of the definitions and Euler's laws of motion. I've modified the line defining the symbol I, to make it clear that I is expressed in the basis provided by R. All other vectors and matrices are expressed in some (any) reference inertial frame. Is it necessary to state this, you think? --Tennenrishin (talk) 16:16, 16 July 2011 (UTC)

Proposed revisions
I would like to work on this article to bring together topics that are distributed among a variety of similarly named articles: analytical dynamics, analytical mechanics, classical mechanics, Lagrangian mechanics, and multi-body dynamics. I think by focusing on rigid body dynamics, I might be able to simplify the presentation, while keeping the mathematical theory that appears in these other pages. Prof McCarthy (talk) 21:58, 2 October 2012 (UTC)