MOTIONS OF A POWERED TOP WITH A SPHERICAL TIP ON A CURVED SURFACE

The purpose of this article is to model the dynamics of a top with a f inite radius tip on a curved basin in a gravitational field without (a nd with) energy addition and dissipation. This is an extension of a ve ry general and classical problem and requires development of a method for treating the dynamical interactions between the two curved surface s. The full nonlinear equations of motion are indicated; however, thes e equations are complex and do not show the dominant mechanisms that d efine the system motions. A novel method of ''partial linearization'' is employed that reduces the equations of motion to a relevant and tra ctable form in which these mechanisms ave clearly exposed. The model a nd related results are compared with relevant examples from the litera ture. The movement of the top is simulated by an integration of the fu lly nonlinear equations of motion and compared with the partially line arized results. (C) 1995 John Wiley & Sons, Inc.