# Dynamics of the Tippe Top via Routhian Reduction

## TL;DR

This paper analyzes the dynamics of a tippe top using Routhian reduction, simplifying the system to classify its steady states and stability properties.

## Contribution

It introduces a Routhian reduction approach to analyze tippe top dynamics, providing a compact classification of steady states and stability.

## Key findings

- Reduced the tippe top system to two dimensions
- Classified tippe tops into six groups based on steady states
- Provided a method to analyze stability of steady states

## Abstract

We consider a tippe top modeled as an eccentric sphere, spinning on a horizontal table and subject to a sliding friction. Ignoring translational effects, we show that the system is reducible using a Routhian reduction technique. The reduced system is a two dimensional system of second order differential equations, that allows an elegant and compact way to retrieve the classification of tippe tops in six groups as proposed in [1] according to the existence and stability type of the steady states.