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.
Mots clés : optimal control, sub-riemannian geometry, differential-geometric methods, left-invariant problem, Lie group, Pontryagin maximum principle, symmetries, exponential mapping, Maxwell stratum
@article{COCV_2010__16_2_380_0, author = {Moiseev, Igor and Sachkov, Yuri L.}, 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://www.numdam.org/articles/10.1051/cocv/2009004/} }
TY - JOUR AU - Moiseev, Igor AU - Sachkov, Yuri L. TI - Maxwell strata in sub-riemannian problem on the group of motions of a plane JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2010 SP - 380 EP - 399 VL - 16 IS - 2 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2009004/ DO - 10.1051/cocv/2009004 LA - en ID - COCV_2010__16_2_380_0 ER -
%0 Journal Article %A Moiseev, Igor %A Sachkov, Yuri L. %T Maxwell strata in sub-riemannian problem on the group of motions of a plane %J ESAIM: Control, Optimisation and Calculus of Variations %D 2010 %P 380-399 %V 16 %N 2 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2009004/ %R 10.1051/cocv/2009004 %G en %F COCV_2010__16_2_380_0
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. http://www.numdam.org/articles/10.1051/cocv/2009004/
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