Prove the following statements about the inertia tensor. Please use rigorous mathematical formulas instead of hand-waving arguments. (a) If the rigid body has a mirror symmetry, and the origin of the coordi- nate lies in the plane of the mirror symmetry, then any axis perpendicular to the mirror-symmetry plane is a principle axis.
Prove the following statements about the inertia tensor. Please use rigorous mathematical formulas instead of hand-waving arguments. (a) If the rigid body has a mirror symmetry, and the origin of the coordi- nate lies in the plane of the mirror symmetry, then any axis perpendicular to the mirror-symmetry plane is a principle axis.
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Transcribed Image Text:Prove the following statements about the inertia tensor. Please use rigorous
mathematical formulas instead of hand-waving arguments.
(a)
If the rigid body has a mirror symmetry, and the origin of the coordi-
nate lies in the plane of the mirror symmetry, then any axis perpendicular
to the mirror-symmetry plane is a principle axis.
(b)
If the rigid body has a a Cn rotational symmetry, then the Cn-symmetric
axis is a principle axis. Cn means rotation of 27/n radians.
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