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Is it possible to directly compute the angles of the axis for the minimum and maximum moments of inertia of this object about the center of mass (or any other point for that matter) without using trial and error to solve the problem by continually rotating the axis until I find the answer?

If so, how?

Note: I am a computer programmer/engineer and although I took a lot of calculus and linear algebra in college, that was a LONG time ago.

thanks