An extended version of the Intermediate Axis Theorem for a freely rotating rigid body

Abstract

Current numerical schemes for 3D rockfall simulation are not able to correctly represent the stability properties of a freely rotating body. Here, we give a proof using Lyapunov functions of an extended intermediate axis theorem, which not only involves the angular momentum equations but also the orientation of the body. Inspired by the stability proof, we present a novel scheme which respects the stability properties of a freely rotating body and which can be incorporated in numerical schemes for the simulation of rigid bodies with frictional unilateral constraints.