ralqs
Nov15-10, 08:15 PM
This is a page from my textbook: http://tinypic.com/r/wbq4k9/7
It says that the products of inertia are unchanged to first order...but they clearly aren't! This is important, because the authors return to this idea repeatedly: that the tensor of inertia remains unchanged to first order for small angular displacements about the principal axes.
Consider: http://tinypic.com/r/b4g3s9/7
This is the author's derivation of Euler's equations. I would think that there should be a contribution from the product of inertia, but there apparently isn't.
So who's wrong: me, or the authors (along with, apparently, Euler and most of the physics community)? I suspect I know, but I can't find any fault with my logic.
It says that the products of inertia are unchanged to first order...but they clearly aren't! This is important, because the authors return to this idea repeatedly: that the tensor of inertia remains unchanged to first order for small angular displacements about the principal axes.
Consider: http://tinypic.com/r/b4g3s9/7
This is the author's derivation of Euler's equations. I would think that there should be a contribution from the product of inertia, but there apparently isn't.
So who's wrong: me, or the authors (along with, apparently, Euler and most of the physics community)? I suspect I know, but I can't find any fault with my logic.