Motions of a Powered Top with a Spherical Tip on a Curved Surface

Abstract

The purpose of this article is to model the dynamics of a top with a finite radius tip on a curved basin in a gravitational field without (and with) energy addition and dissipation. This is an extension of a very general and classical problem and requires development of a method for treating the dynamical interactions between the two curved surfaces. The full nonlinear equations of motion are indicated; however, these equations are complex and do not show the dominant mechanisms that define the system motions. A novel method of “partial linearization” is employed that reduces the equations of motion to a relevant and tractable form in which these mechanisms are clearly exposed. The model and related results are compared with relevant examples from the literature. The movement of the top is simulated by an integration of the fully nonlinear equations of motion and compared with the partially linearized results.