Extremal trajectories and the asymptotics of the Maxwell time in the problem of the optimal rolling of a sphere on a plane
Extremal trajectories and the asymptotics of the Maxwell time in the problem of the optimal rolling of a sphere on a plane
复制标题
球体在平面上最优滚动问题中的极值轨迹和麦克斯韦时间的渐近
DOI：
10.1070/sm2011v202n09abeh004190
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发表时间：
2011
期刊：
影响因子：
--
通讯作者：
Y. Sachkov
中科院分区：
文献类型：
--
作者：
A. Mashtakov;Y. Sachkov
研究了球体在平面上不发生扭转或滑动时的滚动问题。需要将球体从一种接触配置滚动到另一种接触配置，以便接触点所描述的曲线的长度最小。给出了极值轨迹的一种参数化形式。研究了极值轨迹的渐近性和球体在小振幅正弦上滚动的Maxwell时间的性质，得到了这类轨迹的所谓截断时间的估计。参考书目：21种。
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.