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Maxwell strata in sub-Riemannian problemon the group of motions of a plane

Published online by Cambridge University Press:  21 April 2009

Igor Moiseev  and
Yuri L. Sachkov
Igor Moiseev
Affiliation:
Via G. Giusti 1, Trieste 34100, Italy. moiseev.igor@gmail.com
Yuri L. Sachkov
Affiliation:
Program Systems Institute, Pereslavl-Zalessky, Russia. sachkov@sys.botik.ru
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Abstract

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.

Keywords

Optimal controlsub-Riemannian geometrydifferential-geometric methodsleft-invariant problemLie groupPontryagin Maximum Principlesymmetriesexponential mappingMaxwell stratum
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 16 , Issue 2 , April 2010 , pp. 380 - 399
Copyright
© EDP Sciences, SMAI, 2009

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