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

Title: Extremal trajectories and the asymptotics of the Maxwell time in the problem of the optimal rolling of a sphere on a plane
Authors: A. P. Mashtakov, Yu. L. Sachkov
Journal title: Sbornik: Mathematics
Year: 2011
Issue: 9
Volume: 202
Pages: 1347–1371
Citation:

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, 2011, 202:9, 1347–1371

Abstract:

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.