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

Igor Moiseev; Yuri L. Sachkov

ESAIM: Control, Optimisation and Calculus of Variations (2010)

  • Volume: 16, Issue: 2, page 380-399
  • ISSN: 1292-8119

Abstract

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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.

How to cite

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Moiseev, Igor, and Sachkov, Yuri L.. "Maxwell strata in sub-Riemannian problem on the group of motions of a plane." ESAIM: Control, Optimisation and Calculus of Variations 16.2 (2010): 380-399. <http://eudml.org/doc/250752>.

@article{Moiseev2010,
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. },
author = {Moiseev, Igor, Sachkov, Yuri L.},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Optimal control; sub-Riemannian geometry; differential-geometric methods; left-invariant problem; Lie group; Pontryagin Maximum Principle; symmetries; exponential mapping; Maxwell stratum; optimal control; Pontryagin's maximum principle},
language = {eng},
month = {4},
number = {2},
pages = {380-399},
publisher = {EDP Sciences},
title = {Maxwell strata in sub-Riemannian problem on the group of motions of a plane},
url = {http://eudml.org/doc/250752},
volume = {16},
year = {2010},
}

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
DA - 2010/4//
PB - EDP Sciences
VL - 16
IS - 2
SP - 380
EP - 399
AB - 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.
LA - eng
KW - Optimal control; sub-Riemannian geometry; differential-geometric methods; left-invariant problem; Lie group; Pontryagin Maximum Principle; symmetries; exponential mapping; Maxwell stratum; optimal control; Pontryagin's maximum principle
UR - http://eudml.org/doc/250752
ER -

References

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