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.
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  • HAL Id : hal-01475271, version 1
  • OATAO : 17149

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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 (CDC 2013), Dec 2013, Firenze, Italy. pp. 1804-1809. ⟨hal-01475271⟩

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