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

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

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

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topMoiseev, 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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