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

Bernard Bonnard (1) , Olivier Cots (2) , Nataliya Shcherbakova (3)

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]
2 McTAO - Mathematics for Control, Transport and Applications
3 LGC - Laboratoire de Génie Chimique

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.

Domaines: Optimisation et contrôle [math.OC]

Bernard Bonnard, Olivier Cots, Nataliya Shcherbakova. Riemannian metrics on 2D manifolds related to the Euler-Poinsot rigid body problem. 52nd IEEE Conference on Decision and Control, 2013, Firenze, Italy. ⟨hal-00925078v1⟩