DocumentCode
3526617
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
fYear
2013
fDate
10-13 Dec. 2013
Firstpage
1804
Lastpage
1809
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;
fLanguage
English
Publisher
ieee
Conference_Titel
Decision and Control (CDC), 2013 IEEE 52nd Annual Conference on
Conference_Location
Firenze
ISSN
0743-1546
Print_ISBN
978-1-4673-5714-2
Type
conf
DOI
10.1109/CDC.2013.6760144
Filename
6760144
Link To Document