FTP, what is this tensor, whose eigenvalues are analogous to mass for rotational motion, usually symbolized with a capital I?
The largest and smallest of its eigenvalues correspond to stable motion, but the middle one to unstable motion, according to the tennis racket theorem.  Diagonalization of this quantity gives the principle axes of the system, and when it operates on an angular velocity vector the result is the net torque.  It has a beta of two-thirds for a spherical shell and two-fifths for a solid sphere about their centers, and one-half for a solid disk.  FTP, what is this tensor, whose eigenvalues are analogous to mass for rotational motion, usually symbolized with a capital I?
The largest and smallest of its eigenvalues correspond to stable motion, but the middle one to unstable motion, according to the tennis racket theorem.  
moment of inertia or inertial moment tensor