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arXiv · 2411.09008

Integrable sub-Riemannian geodesic flows on the special orthogonal group

Alejandro Bravo-Doddoli·Philip Arathoon·Anthony M. Bloch
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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 $n$-dimensional rigid body: namely, by exhibiting a Lax pair and bi-Hamiltonian structure for the reduced equations of motion.

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Alejandro Bravo-Doddoli, Philip Arathoon, Anthony M. Bloch. 2024-11-13. Integrable sub-Riemannian geodesic flows on the special orthogonal group. https://arxiv.org/abs/2411.09008

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