Dynamics of the Tippe Top -- properties of numerical solutions versus the dynamical equations

TL;DR

This paper investigates the relationship between numerical simulations and the underlying dynamical equations of the Tippe Top, revealing oscillatory behavior and detailed features of its inversion process.

Contribution

It provides a detailed comparison of numerical solutions with the theoretical dynamical equations, enhancing understanding of the Tippe Top's inversion dynamics.

Findings

Numerical solutions confirm oscillatory inclination angle behavior.

Fine features of inversion are identified and partially explained.

The study links numerical results with theoretical dynamics.

Abstract

We study the relationship between numerical solutions for inverting Tippe Top and the structure of the dynamical equations. The numerical solutions confirm oscillatory behaviour of the inclination angle $\theta(t)$ for the symmetry axis of the Tippe Top. They also reveal further fine features of the dynamics of inverting solutions defining the time of inversion. These features are partially understood on the basis of the underlying dynamical equations.