旋转平面上Chaubergin球的动力学
Dynamics of the Chaplygin ball on a rotating plane
摘要：
本文研究了在水平面上以恒定角速度旋转的Chaubergin球的滚动问题。在这种情况下，运动方程允许面积积分，平方角动量的积分和雅可比积分，这是能量积分的推广，并拥有不变测度。减少后的问题减少到调查一个三维庞加莱映射，保留相体积（密度定义的不变措施）。我们表明，在一般情况下，系统的动力学是混沌的。
英文摘要：
This paper addresses the problem of the Chaplygin ball rolling on a horizontal plane which rotates with constant angular velocity. In this case, the equations of motion admit area integrals, an integral of squared angular momentum and the Jacobi integral, which is a generalization of the energy integral, and possess an invariant measure. After reduction the problem reduces to investigating a three-dimensional Poincare map that preserves phase volume (with density defined by the invariant measure). We show that in the general case the system's dynamics is chaotic.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
