Geodesic
Extremal trajectories and the asymptotics of the Maxwell time in the problem of the optimal rolling of a~sphere on a~plane
Sbornik. Mathematics, Tome 202 (2011) no. 9, pp. 1347-1371

Voir la notice de l'article provenant de la source Math-Net.Ru

The problem of a sphere rolling on a plane without twisting or slipping is considered. It is required to roll the sphere from one contact configuration to another so that the length of the curve described by the contact point is minimal. A parametrization of extremal trajectories is obtained. The asymptotics of extremal trajectories and the behaviour of the Maxwell time for the rolling of a sphere over sinusoids of small amplitude are studied; for such trajectories estimates for the so-called cut time are obtained. Bibliography: 21 titles.
Keywords: optimal control, geometric methods, symmetries of the exponential map, rolling of surfaces, Euler elastics. 
@article{SM_2011_202_9_a4,
     author = {A. P. Mashtakov and Yu. L. Sachkov},
     title = {Extremal trajectories and the asymptotics of the {Maxwell} time in the problem of the optimal rolling of a~sphere on a~plane},
     journal = {Sbornik. Mathematics},
     pages = {1347--1371},
     publisher = {mathdoc},
     volume = {202},
     number = {9},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2011_202_9_a4/}
}
TY  - JOUR
AU  - A. P. Mashtakov
AU  - Yu. L. Sachkov
TI  - Extremal trajectories and the asymptotics of the Maxwell time in the problem of the optimal rolling of a~sphere on a~plane
JO  - Sbornik. Mathematics
PY  - 2011
SP  - 1347
EP  - 1371
VL  - 202
IS  - 9
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_2011_202_9_a4/
LA  - en
ID  - SM_2011_202_9_a4
ER  - 
%0 Journal Article
%A A. P. Mashtakov
%A Yu. L. Sachkov
%T Extremal trajectories and the asymptotics of the Maxwell time in the problem of the optimal rolling of a~sphere on a~plane
%J Sbornik. Mathematics
%D 2011
%P 1347-1371
%V 202
%N 9
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_2011_202_9_a4/
%G en
%F SM_2011_202_9_a4
A. P. Mashtakov; Yu. L. Sachkov. Extremal trajectories and the asymptotics of the Maxwell time in the problem of the optimal rolling of a~sphere on a~plane. Sbornik. Mathematics, Tome 202 (2011) no. 9, pp. 1347-1371. http://geodesic.mathdoc.fr/item/SM_2011_202_9_a4/