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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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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/

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