Maxwell strata in sub-Riemannian problem on the group of motions of a plane
Via G. Giusti 1, Trieste 34100, Italy. firstname.lastname@example.org
2 Program Systems Institute, Pereslavl-Zalessky, Russia. email@example.com
The left-invariant sub-Riemannian problem on the group of motions of a plane is considered. Sub-Riemannian geodesics are parameterized by Jacobi's functions. Discrete symmetries of the problem generated by reflections of pendulum are described. The corresponding Maxwell points are characterized, on this basis an upper bound on the cut time is obtained.
Mathematics Subject Classification: 49J15 / 93B29 / 93C10 / 53C17 / 22E30
Key words: Optimal control / sub-Riemannian geometry / differential-geometric methods / left-invariant problem / Lie group / Pontryagin Maximum Principle / symmetries / exponential mapping / Maxwell stratum
© EDP Sciences, SMAI, 2009