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

Bernard Bonnard, Olivier Cots, Nataliya Shcherbakova

Type: Preprint

Publication Date: 2013-12-01

Citations: 2

DOI: https://doi.org/10.1109/cdc.2013.6760144

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.

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