- #1
VuIcan
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Hello, I've just been slightly unsure of something and would like to get secondary confirmation as I've just begun a book on tensor analysis. I would also preface this by saying my linear algebra is somewhat rusty. Suppose you have the inertia tensor in some unprimed coordinate system such that ##\mathbf{\widetilde{I}}##, then we know definitionally that this second-rank tensor will transform as such to into some primed coordinate system(where ##\Lambda## corresponds to the transformation matrix from the unprimed to the primed coordinate system):
$$ \widetilde{I}' = \Lambda \widetilde{I} \Lambda ^{\dagger}$$
Now, if one were to apply some vector stimulus in the primed coordinate system from the right, would it be correct to think of this vector as firstly being transformed into the unprimed coordinate system (since the adjoint is equivalent to the inverse within this context), then being directionally altered by the inertia tensor in the unprimed coordinate system, then finally being transformed back into the primed coordinate system by the final matrix? I feel like I'm misunderstanding something fundamental however.
Thanks in advance,
-Vulcan
$$ \widetilde{I}' = \Lambda \widetilde{I} \Lambda ^{\dagger}$$
Now, if one were to apply some vector stimulus in the primed coordinate system from the right, would it be correct to think of this vector as firstly being transformed into the unprimed coordinate system (since the adjoint is equivalent to the inverse within this context), then being directionally altered by the inertia tensor in the unprimed coordinate system, then finally being transformed back into the primed coordinate system by the final matrix? I feel like I'm misunderstanding something fundamental however.
Thanks in advance,
-Vulcan