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

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.