# Talk:Euler's laws of motion

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## Symbol convention used

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)

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)
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)
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)

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)

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, $\tau$ = 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)
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)
Ok - done, except I kept M for torque/moment (synonyms), easier to use instead of $\boldsymbol{\tau}, \boldsymbol{\Gamma}$ etc. If anyone notices any more unexplained notation just say so. Maschen (talk) 21:59, 20 August 2012 (UTC)

## Incorrect formula for "force density"

There is the incorrect claim that this:

$\mathbf F_B=\int_V\mathbf b\,dm=\int_V \rho\mathbf b\,dV$

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:

$\mathbf F_B=\int_V\mathbf b\,dV = \int_V\mathbf b\,\frac{dm}{\rho}$

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)

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 $\mathbf{F}$ 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 $\partial$R. Any volume element dV experiences a long-range force $\rho$b dV , where $\rho$is the density (mass per unit volume) and $\mathbf{b}$ is a vector field (with dimensions of force per unit mass) called the body force. Any oriented surface element $d\mathbf{S}$ = $\mathbf{n}dS$ experiences a contact force $\mathbf{t}(\mathbf{n})dS$, where $\mathbf{t}(\mathbf{n})$ 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 $\mathbf{n}$.

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

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)
I fixed it up according to the source.Maschen (talk) 07:13, 21 August 2012 (UTC)
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)
...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)