Discrete Spinning Tops -- Difference equations for Euler, Lagrange, and Kowalevski tops

TL;DR

This paper explores various time discretization methods for integrable rigid body models like Euler, Lagrange, and Kowalevski tops, introducing a new discretization approach for the Kowalevski top that preserves key properties.

Contribution

A novel discretization method for the Kowalevski top that exactly preserves its integrals and properties, with successful numerical validation.

Findings

New discretization method preserves Kowalevski top properties

Numerical tests confirm method's effectiveness

Discussion of Lax-Moser pairs and conservation laws

Abstract

Several methods of time discretization are examined for integrable rigid body models, such as Euler, Lagrange, and Kowalevski tops. Problems of Lax-Moser pairs, conservation laws, and explicit solver algorithms are discussed. New discretization method is proposed for Kowalevski top, which have properties $\boldsymbol{\gamma}^2=1$, and the Kowalevski integral $|\xi|^2=\text{const.}$ satisfied exactly. Numerical tests are done successfully.