Precession of the Kovalevskaya and Goryachev-Chaplygin tops

TL;DR

This paper analyzes the precession behavior of Kovalevskaya and Goryachev-Chaplygin tops using analytical and numerical methods, revealing conditions for zero or estimable average precession change based on topological insights.

Contribution

It provides new analytical and numerical insights into the precession dynamics of these integrable tops, linking topological properties to precession behavior.

Findings

Identified initial conditions with zero average precession change.

Developed asymptotic estimates for precession in certain cases.

Performed numerical studies on complex precession scenarios.

Abstract

The change of the precession angle is studied analytically and numerically for the integrable tops of Kovalevskaya and Goryachev-Chaplygin. Based on the known results on the topology of Liouville foliations for these systems, we find initial conditions for which the average change of the precession angle is zero or can be estimated asymptotically. Some more difficult cases are studied numerically.