Talk:Newton–Euler equations

This article needs a short introduction explaining what this is about.Ben Finn 23:11, 27 October 2005 (UTC)

The form of the newton-euler equations in this article for a reference frame that is not coincident with center of mass are ONLY correct if there is NO relative velocity between this reference frame and the center of mass. This means the reference point for these Equ. has to be fixed to the rigid body.

This is because you need to replace \dot{\vec{c}} by \vec{\omega}\times\vec{c} to obtain these equations and this is only possible if c is constant for a body-fixed reference frame.

Sorry for my bad english. — Preceding unsigned comment added by 88.217.117.125 (talk) 23:50, 29 October 2011 (UTC)

I believe this article is misleading by calling J_c the moment of inertia about the CM. This description implies it is an inertia tensor with the product of inertias equal to zero (i.e. only moment of inertias, hence being called "the moment of inertia about..."). However, even with a CM coordinate, your axes may not be principal axes, and your product of inertias may not be zero. So I would call J_c the inertia tensor, which describes more fully that the product of inertias are not necessarily zero. I also think the article is very vague to someone new to the topic -- it doesn't even define the dimensions of the vectors! Aghez (talk) 00:31, 31 March 2012 (UTC)

I am planning to add a section giving the derivation of these equations. To improve readability, I would also like to replace the cross product matrix notation $$[{\mathbf c}]^{\times}$$ with the more concise $$[{\mathbf c}]$$. JAELloyd (talk) 08:35, 21 April 2015 (UTC)

This sounds like a good addition. We need to amend this page with the equations of motion expressed on a point away from the center of mass. I have an accepted answer on Physics Stackexchange Answer 1 deriving this expression. In addition, the explicit expression for the inverse spatial inertia can be added as seen in Edit 1 of Physics Stackexchange Answer 2. User Aghez has a good point about needing to transform the inertia matrix from body coordinates to world coordinates before they can be used. iou (talk) 23:36, 21 April 2015 (UTC)