Integrable geodesic flows of non-holonomic metrics

Details Integrable geodesic flows of non-holonomic metrics Integrable geodesic flows of non-holonomic metrics

1996-10-23

arxiv.org/abs/dg-ga/9610012v1

J. Dynam. Control Systems 3 (1997), 129--147.

Mathematics

Differential Geometry

15 pages, LaTeX

Scientific paper

Normal geodesic flows flows of Carnot-Caratheodory are discussed from the point of view of the theory of Hamiltonian systems. The geodesic flows corresponding to left-invariant metrics and left- and -right-invariant rank 2 distributions on the three-dimensional Heisenberg group are analysed as integrable systems. The flows corresponding to left-invariant metrics and left-invariant distributions on Lie groups are reduced to Euler equations on Lie groups. Relation of these constructions to problems of analytical mechanics is discussed.

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