why principal axis is called the eigenvector of moment of inertia tensor

Dear Renu

 

A principal axis of rotation (or principal direction) is an eigenvector of the mass moment of inertia tensor defined relative to some point (typically the centre of mass). The corresponding eigen values are called the principal moments of inertia.. Because the moment of inertia tensor is defined relative to the point x = 0 in the space, the principal axes all pass through that point (usually the center of mass).

Hence principal axis is called the eigenvector of moment of inertia tensor.

 

Regards

Arun (askIITians forum expert)