Article contents
Riemannian metrics on 2D-manifolds related to the Euler−Poinsot rigid body motion∗
Published online by Cambridge University Press: 10 June 2014
Abstract
The Euler−Poinsot rigid body motion is a standard mechanical system and it is a model for left-invariant Riemannian metrics on SO(3). In this article using the Serret−Andoyer variables we parameterize the solutions and compute the Jacobi fields in relation with the conjugate locus evaluation. Moreover, the metric can be restricted to a 2D-surface, and the conjugate points of this metric are evaluated using recent works on surfaces of revolution. Another related 2D-metric on S2 associated to the dynamics of spin particles with Ising coupling is analysed using both geometric techniques and numerical simulations.
Keywords
- Type
- Research Article
- Information
- ESAIM: Control, Optimisation and Calculus of Variations , Volume 20 , Issue 3 , July 2014 , pp. 864 - 893
- Copyright
- © EDP Sciences, SMAI, 2014
References
- 8
- Cited by