Basically the rotation of any 3D rigid object can be reduced to the rotation of an equivalent ellipsoid. The lengths of the three principle axes of the ellipsoid determine the moment of intertia around that axis.
For the case where the three principle axes are different lengths, the rotation is only stable around the smallest and biggest axis.
Ie, in a tennis racket you can easily spin the racket around the axis of the handle, and also the axis that is perpendicular to the plane of the netting.
But the racket won't easily spin in the axis perpendicular to these two.
We saw this as a demo in my undergrad classical mechanics class using a book (where the three axis are a bit easier to see since a book is more uniform).
Basically the rotation of any 3D rigid object can be reduced to the rotation of an equivalent ellipsoid. The lengths of the three principle axes of the ellipsoid determine the moment of intertia around that axis.
For the case where the three principle axes are different lengths, the rotation is only stable around the smallest and biggest axis.
Ie, in a tennis racket you can easily spin the racket around the axis of the handle, and also the axis that is perpendicular to the plane of the netting.
But the racket won't easily spin in the axis perpendicular to these two.
We saw this as a demo in my undergrad classical mechanics class using a book (where the three axis are a bit easier to see since a book is more uniform).