The motion of a sphere with weak nutation on a rough horizontal plane

Abstract

For the motion of a sphere on a rough horizontal plane, in the previous paper [1], the author aimed at providing approximate analytical solutions while 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.