Major-axis relaxation theorem ($T\ge L^2/(2I_{\max })$)

At fixed angular momentum, rotational energy is minimized by rotation about the largest principal moment of inertia. Indeed, $T={\sum }_i{L}_i^2/(2I_i)\ge {\sum }_i{L}_i^2/(2I_{\max })$. Weak internal dissipation can therefore relax a nearly rigid isolated body towards that axis. A perfectly rigid torque-free body conserves energy and does not settle; both extreme-inertia axes are stable in its ideal dynamics. The maximum-inertia axis need not be the geometrically longest axis.