Talk:Euler's equations (rigid body dynamics)

$$\mathbf{\omega}$$ - is obvously not a "... rate of change of Euler angles ..." the relation between angular velosity and derivatives of Euler angles is rather complicated. It is also well known, that the usage of any set of Euler angles lead to singularity of this transformation at some orientation of the body with respect to the space-fixed reference frame (or lab R.F.). Usage of quaternions as rotation parameters removes this problem (see Goldstein).

The article is generaly messy. Needs major rewriting.

Leonid Paramonov, Imperial College London 06/12/2005

iam asking about wave speed in thick pipe

Hi

sorry to revert your edits but the term "body fixed axes" is standard nomenclature. Perhaps it should be "body-fixed axes" tho?

best wishes

Robinh 20:30, 4 September 2005 (UTC)


 * Thanks for explaining (it seems like most reverters don't bother.) You're right - I found "body fixed axes" and "body-fixed axes" in Google, and I must have missed it last night. Body-fixed makes more sense to me - it makes it clear that "body" is modifying the word "fixed" and I probably wouldn't have messed with it. I presume you don't object to my other changes you reverted, such as correcting "equotations". Art LaPella 22:17, September 4, 2005 (UTC)
 * Hi Art. No probs.  I didn't see the lower-down edits (my screen must be too small ;-).  I must say I'm astonished that LHS had a wiki link; one learns something every day.  Best wishes Robinh 07:13, 5 September 2005 (UTC)

"where Q is the rotation tensor (not a rotation matrix)"
It seems to me that in that part of the article, Q is indeed the rotation matrix, sometimes called the rotation tensor, which transforms vectors in one frame to another by preserving angles and lengths. And isn't the matrix involving angular momentum components. Very confusing! Here is a reference, see equation (18) and the discussion around it. https://rotations.berkeley.edu/kinematics-of-rigid-bodies/ 2600:1700:BA69:10:6EBA:2BD4:9FD7:913E (talk) 20:12, 12 August 2022 (UTC)

Analytical solution
it could be included analytical solutions for the equations in some cases. For asymmetric objects the solution is based on Jaboc Elliptical Functions (as can be checked in Landau and Liftshiftz Theoretical Physics V1) KaboomPhysicist (talk) 03:16, 24 August 2022 (UTC)