  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.
