Journal
ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS
Volume 16, Issue 2, Pages 380-399Publisher
CAMBRIDGE UNIV PRESS
DOI: 10.1051/cocv/2009004
Keywords
Optimal control; sub-Riemannian geometry; differential-geometric methods; left-invariant problem; Lie group; Pontryagin Maximum Principle; symmetries; exponential mapping; Maxwell stratum
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Funding
- Russian Foundation for Basic Research [09-01-00246-a]
- Presidium of Russian Academy of Sciences
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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.
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