Geodesic
Maxwell strata in sub-riemannian problem on the group of motions of a plane
ESAIM: Control, Optimisation and Calculus of Variations, Tome 16 (2010) no. 2, pp. 380-399

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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.

DOI : 10.1051/cocv/2009004
Classification : 49J15, 93B29, 93C10, 53C17, 22E30
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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     title = {Maxwell strata in sub-riemannian problem on the group of motions of a plane},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {380--399},
     publisher = {EDP-Sciences},
     volume = {16},
     number = {2},
     year = {2010},
     doi = {10.1051/cocv/2009004},
     mrnumber = {2654199},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2009004/}
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Moiseev, Igor; Sachkov, Yuri L. Maxwell strata in sub-riemannian problem on the group of motions of a plane. ESAIM: Control, Optimisation and Calculus of Variations, Tome 16 (2010) no. 2, pp. 380-399. doi: 10.1051/cocv/2009004

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