The Analytical Method of the Mechanics Problem Involving a Hyperelliptic Integral

Abstract

It is extremely difficult to obtain the analytical solution of some mechanical problems related to elliptic integrals. The motion of a small ball that rolls without sliding on a smooth hemisphere is a typical hyperelliptic integral problem of this kind. By utilizing elliptic integration theory and operational skills, we give the analytical method of the solution of the motion law of the small ball. At the same time, we exhibit the motion characteristic of the small ball.