Title :
Riemannian metrics on 2D manifolds related to the Euler-Poinsot rigid body problem
Author :
Bonnard, Bernard ; Cots, Olivier ; Shcherbakova, Nataliya
Author_Institution :
Inst. de Math. de Bourgogne, Univ. de Bourgogne, Dijon, France
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.
Keywords :
Jacobian matrices; numerical analysis; shear modulus; 2D manifolds; Euler-Poinsot rigid body problem; Jacobi fields; SO(3); Serret-Andoyer reduction; conjugate loci; coupled spins; left-invariant metrics; numerical results; spin dynamics; subRiemanian metrics; Equations; Jacobian matrices; Measurement; Optimal control; Standards; Trajectory; Vectors;
Conference_Titel :
Decision and Control (CDC), 2013 IEEE 52nd Annual Conference on
Conference_Location :
Firenze
Print_ISBN :
978-1-4673-5714-2
DOI :
10.1109/CDC.2013.6760144
