Integrable sub-Riemannian geodesic flows on the special orthogonal group
Differential Geometry
2025-08-19 v3 Dynamical Systems
Abstract
We analyse the geometry of the rubber-rolling distribution on the special orthogonal group and show that almost all the normal geodesics of any right-invariant sub-Riemannian metric defined on this distribution are completely integrable. Our argument is an adaptation of the method used to establish integrability of the Riemannian metric arising from the -dimensional rigid body: namely, by exhibiting a Lax pair and bi-Hamiltonian structure for the reduced equations of motion.
Cite
@article{arxiv.2411.09008,
title = {Integrable sub-Riemannian geodesic flows on the special orthogonal group},
author = {Alejandro Bravo-Doddoli and Philip Arathoon and Anthony M. Bloch},
journal= {arXiv preprint arXiv:2411.09008},
year = {2025}
}