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Maxwell strata in sub-Riemannian problem on the group of motions of a plane. (English) Zbl 1217.49037

Summary: 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.

MSC:

49Q20 Variational problems in a geometric measure-theoretic setting
49J15 Existence theories for optimal control problems involving ordinary differential equations
93B27 Geometric methods
93C10 Nonlinear systems in control theory
53C17 Sub-Riemannian geometry
22E30 Analysis on real and complex Lie groups
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References:

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