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exponential mapping

ESAIM: Control, Optimisation and Calculus of Variations (1)

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Maxwell strata in sub-Riemannian problemon the group of motions of a plane
Igor Moiseev, Yuri L. Sachkov
Journal:

ESAIM: Control, Optimisation and Calculus of Variations / Volume 16 / Issue 2 / April 2010

Published online by Cambridge University Press:

21 April 2009, pp. 380-399

Print publication:

April 2010
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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.