Utilization of Maple-based Physics Computation in Determining the Dynamics of Tippe Top

Abstract

Tippe top is an example of simple moving system of rigid body with non-holonomic constraint, but the analysis of this system is not simple. A tippe top equation has been derived with Routhian reduction method and Poincaré equation, and physics computation in finding numeric solution of the dynamics of the tippe top has also been utilized by using Maple program. However, the Poincaré equation required that quasi-coordinate of the quasi-velocity is found, while in the case of the dynamics of tippe top, there is not any exact solution of the quasi-coordinate of the quasi-velocity was found. Therefore, the tippe top equation should be reduced to solve the problem. In this research, Routhian reduction was employed so that the Routhian reduction-based Poincaré equation was used to derive the tippe top equation. The method was able to derive a tippe top equation on a flat plane and tube inner surface clearly represented differential equations.