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本文讨论微粗糙水平面上旋转的非均质球形刚体的全局运动.用摄动法分析刚球在非线性滑动摩擦力作用下的运动规律.分析表明,刚球存在三种可能的稳态运动,即质心低于或高于球心绕对称轴作永久转动,或以某个确定章动角作规则进动.文中导出各稳态运动的稳定性判据,并讨论进动角速度的变化对刚球全局运动特征的影响以及由此产生的分叉现象.文中还对刚球快速旋转的特殊情形,导出非线性运动方程的解析积分,以验证定性分析结果的正确性.
In this paper, the global motion of a non-homogeneous spherical rigid body rotating on a micro rough surface is discussed. The perturbation method is used to analyze the motion of a rigid spherical ball under the nonlinear sliding friction. The analysis shows that there are three possible steady- That is, the center of mass is lower or higher than the center of the ball for a permanent rotation around the axis of symmetry or a certain fixed nutation angle for regular precession.The stability criterion of steady-state motions is deduced and the change of precession angular velocity is discussed. The global motion of the ball and the resulting bifurcation phenomenon.The article also derives the analytic integral of the nonlinear equation of motion for the special case of the fast rotation of the rigid ball to verify the correctness of the qualitative analysis results.