Consider a rigid body and the (at least) three axes of inertia passing through its center of mass.

Will any other axis not passing through the center of mass but parallel to one of the principal axes passing through the CM, still be a principal axis of inertia? And why does this happen?

  • $\begingroup$ No principal axes of inertia only go through the center of mass. $\endgroup$ – John Alexiou Apr 19 '16 at 18:02

The 3×3 mass moment of inertia matrix only conveys information about the orientation of the principal axes and not their location. Their location is by definition on the center of mass.

It is true that if rotating about an axis parallel to one of the principal axes, but not about the center of mass the MMOI matrix is world coordinates can still be diagonal even after the application of the parallel axis theorem.

But because this rotation is not about the center of mass, there will be cross-terms in acceleration forcing the center of mass to prescribe an orbit around the rotation axis.

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