Dynamic Analysis of Tippe Top on Cylinder’s Inner Surface With and Without Friction based on Routh Reduction

Abstract

Physics computing can be used to help to solve complex dynamic equations, both translation and rotation. The purpose of this study was to obtain differences in the dynamics of the tippe top with and without friction moving on inner surface of a cylindrical with varying initial state based of Routhian Reduction. The equation of tippe top in flat fields with and without friction has been reduced by the Routhian reduction method with the Poincare equation with computational in the previous research, and computation has also been carried out in the search for numerical solutions to the dynamics of tippe top with friction in the Maple program. In this study the reduction used is a Routhian reduction, so that the equation used in determining the equations of tippe top motion with and without friction that moves in a curved plane in the form of a cylindrical surface with varying initial state based on maple is Poincaré’s equation based on Routhian reduction with and without friction. The effect of friction can be seen clearly through the dynamics and graph equations in the return top. This method can reduce the equation of backward motion with and without friction that moves on the surface of the cylinder clearly in the form of a set of differential equations. This research can be continued by solving the dynamic equations of the tippe top in other curved fields such as the torus and ball. The findings of this study are dynamic equations and graphs of friction with and without friction equations that move in curved fields in the inner of surfaces in cylinders with varying initial state based on maple.