带有微弱章动的圆球在粗糙水平面上的运动

The Motion of a Sphere with Weak Nutation on a Rough Horizontal Plane

对于圆球在粗糙水平面上的运动，在文［１］中，作者忽略了章动，得到了近似解析解．本文在此基础上给出了有章动情况下的控制方程．通过求解这些方程，证明文［１］关于接触点速度的结论在有章动时仍然正确．还得到其它一些有趣的结果，例如：球心和接触点的速度与球的自转角速度和章动角速度有一定联系；球心和接触点的速度的方向具有不变性．在进一步假设微弱章动的情况下，文中得到近似解析解，从而证明文［１］结果的正确性．

For the motion of a sphere on a rough horizontal plane,in the previous paper[1],the author aimed at providing approximate analytical solutions wliile the nutation is neglected.In this paper,the control equations for the sphere with nutation have been deduced on the basis of paper[1].Through the medium of solving these equations, the conclusion for the velocity of contact point in paper [1] is still proved true for the case with nutation. What is more,some interesting results are gained,for example,the velocity of centre and contact point is relative to the angular velocity of spin and nutation; the direction of velocity of centre and contact point is constant.Under the condition which is supposed to be weak nutation,the approximate analytical solutions are obtained,so that the results of paper[1] is proved to be true.