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 ${\mathit{\gamma }}^2=1$, and the Kowalevski integral $\mathrm{\mid }\xi {\mathrm{\mid }}^2=\text{const.}$ satisfied exactly. Numerical tests are done successfully.