Talk:Euler's laws of motion

Latest comment: 6 years ago by AndrewDressel in topic Euler's laws also hold for a continuum

Symbol convention used

edit

An editor just changed the symbol for angular momentum from L to H in the initial statement of Euler's Second Law. That avoids the conflict with the use of L for angular momentum in the statement of the first law and might have been fine, but L is also used throught the rest of the article for angular momentum. I propose that we go with the most reliable source already used in the article and that is available online anyone to check: Dynamics of particles and rigid bodies: a systematic approach by Anil Vithala Rao. He uses G for linear momentum and H for angular momentum. Comments? -AndrewDressel (talk) 17:57, 8 November 2010 (UTC)Reply

Since L for angular & p for linear momentum is pretty much the standard in physics, I don't see why we can't just use these, it would make it easier to follow & would by no means be original research. JIMp talk·cont 09:15, 31 January 2011 (UTC)Reply
First, thanks for the reply. I had forgotten all about this issue. Next, this article was originally written and referenced from the point of view of Engineering Mechanics, not physics. Though both are perfectly valid, as with flavors of English, I believe the original language should be maintained, unless there is a compelling reason to change it. Finally, the physics textbooks I have seen also use P for power. I like the convention used by Ruina and Pratap: L for linear momentum and H for angular momentum. They reserve G for center of mass and also use P for power. -AndrewDressel (talk) 14:55, 31 January 2011 (UTC)Reply
On the other hand, if we look at the categories that the article has been put into, it seems more like a physics article. Sticking to the original flavour is generally best. L for linear momentum would be particularly confusing since that's used for angular momentum in physics. JIMp talk·cont 21:14, 31 January 2011 (UTC)Reply

Hello, there's several equations in this article in which the terms (I,T,S, and other greek symbols) are not defined. i'm a begining student trying to figure out the text. can someone make some revisions please? — Preceding unsigned comment added by Mikewax (talkcontribs) 18:46, 18 March 2012 (UTC)Reply

Will do. Agreed about the symbol convention mentioned above in the article. It would be much simpler to use p = linear momentum, L = angular momentum, F for force,   = torque, etc... aka all the standard symbols. Is the funny convention of G, = linear momentum, H = angular momentum etc in the sources? Will check soon... Maschen (talk) 20:50, 20 August 2012 (UTC)Reply
WTF was I thinking??... As indicated by others above G and H are used in the sources... I think its best to use the common notation just stated for common usage with other articles like Euler's equations (rigid body dynamics), and include a couple of notes saying "G is also used for linear momentum" and "H is also used for angular momentum" as and when etc... Maschen (talk) 21:38, 20 August 2012 (UTC)Reply
Ok - done, except I kept M for torque/moment (synonyms), easier to use instead of   etc. If anyone notices any more unexplained notation just say so. Maschen (talk) 21:59, 20 August 2012 (UTC)Reply

Incorrect formula for "force density"

edit

There is the incorrect claim that this:

 

is the force density acting on a rigid body. This has the dimensions of [force]·[volume]−1·[mass] = [mass]·[volume]−1[force]·[volume]−1·[volume] = [mass]·[force]·[volume]−1 ≠ [force]·[volume]−1. If b is the force density, then this is integrated over the volume of the body:

 

It's just simple dimensional analysis. All the factors of ρ for mass density are wrong. Will fix... Maschen (talk) 21:26, 20 August 2012 (UTC)Reply

You may need to read the referenced book "Plastic Theory", pg 27-28, by Jacob Lubliner. The content in those pages defines the variables used in this equation:

The total force   on a body B is thus the vector sum of all the forces exerted on it by all the other bodies in the universe. In reality these forces are of two kinds: long-range and short-range. If B is modeled as a continuum occupying a region R, then the effect of the long-range forces is felt throughout R, while the short-range forces act as contact forces on the boundary surface  R. Any volume element dV experiences a long-range force  b dV , where  is the density (mass per unit volume) and   is a vector field (with dimensions of force per unit mass) called the body force. Any oriented surface element   =   experiences a contact force  , where   is called the surface traction; it is not a vector field because it depends not only on position but also on the local orientation of the surface element as defined by the local value (direction) of  .

--LaoChen (talk) 01:09, 21 August 2012 (UTC)Reply

So you’re saying b is force per unit mass, which is acceleration? It was not clear from the initial article. It seems correct that your t(n) is a pseudovector field if it has the form t × n (which takes into account the orientation as you said), but this was not in the article: in the force expression dS usually T refers to the stress-energy tensor...
I'm not sure of the relevance of "long-range forces", aren’t they negligible (force by any distant Galaxy on any Earth bound object negligible in comparison to the weight acting on that object due to the Earth)? I thought the forces acting on the rigid body were taken in this article to be throughout the volume V (volume integral) and on the surface S (surface integral). Nothing to do with "long/short range forces"... Maschen (talk) 06:52, 21 August 2012 (UTC)Reply
I fixed it up according to the source.Maschen (talk) 07:13, 21 August 2012 (UTC)Reply
These more advanced equations are used in the context of plasticity theory, which may be a bit challenging for the high school students trying to learn the laws of classical mechanics.--LaoChen (talk)23:19, 21 August 2012 (UTC)Reply
...which the article does already because the equations are stated upfront, with the plasticity equations after Euler's laws for sake of application. What's your point? Maschen (talk) 18:34, 17 September 2012 (UTC)Reply
edit

Hello fellow Wikipedians,

I have just modified one external link on Euler's laws of motion. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:

When you have finished reviewing my changes, you may follow the instructions on the template below to fix any issues with the URLs.

This message was posted before February 2018. After February 2018, "External links modified" talk page sections are no longer generated or monitored by InternetArchiveBot. No special action is required regarding these talk page notices, other than regular verification using the archive tool instructions below. Editors have permission to delete these "External links modified" talk page sections if they want to de-clutter talk pages, but see the RfC before doing mass systematic removals. This message is updated dynamically through the template {{source check}} (last update: 5 June 2024).

  • If you have discovered URLs which were erroneously considered dead by the bot, you can report them with this tool.
  • If you found an error with any archives or the URLs themselves, you can fix them with this tool.

Cheers.—InternetArchiveBot (Report bug) 15:17, 24 September 2017 (UTC)Reply

Euler's laws also hold for a continuum

edit

As discussed in the article on continuum mechanics, Euler's laws also hold for deformable continua. They are results derivable from conservation of mass, linear momentum, and angular momentum. I propose to modify the first sentence of this article to reflect this fact.128.32.164.33 (talk) 23:47, 3 November 2017 (UTC)Reply

Provide a reliable source and have at it. -AndrewDressel (talk) 23:50, 3 November 2017 (UTC)Reply