Riemannian metrics on 2D manifolds related to the Euler-Poinsot rigid body problem

Abstract

The Euler-Poinsot rigid body problem is a well known model of left-invariant metrics on SO(3). In the present paper we discuss the properties of two related reduced 2D models: the sub-Riemanian metric of a system of three coupled spins and the Riemannian metric associated to the Euler-Poinsot problem via the Serret-Andoyer reduction.We explicitly construct Jacobi fields and explain the structure of conjugate loci in the Riemannian case and give the first numerical results for the spin dynamics case.