Four point objects, each of mass m, are arranged at the corners of a regular tet

Question

Four point objects, each of mass m, are arranged at the corners of a regular tetrahedron with Cartesian coordinates ns shown in the figure below, where a is a constant length. The four Objects rotate together as a rigid body so that they always maintain a tetrahedral arrangement. Figure 2: Four point-object system 1. Using tile coordinate system shown in the figure, work out the inertia tensor. They answer should he a 3 x 3 matrix. 2. Work out the normal vectors along the three principal axes of the system about the origin O. Find out the corresponding principal moments of inertia. (hint: Two of the three principal moments of inertia should have the same value while the other one is different.)

Explanation / Answer

think it's reducing 9 rotation axes to 3 components by finding the eigenvectors, so finding the three (orthogonal, likely), uncorrelated axes into which all rotations in the entire space can be decomposed.

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