A Comparison Between Some Approximate and Numerical Solution of Dynamical Eulerliouville Equation for Rigid Non-Symetrical Free Body with Fast Oscilating Interaction in Gravitational Field

Tumbling NPA (non-principal axis) asteroids are discovered by the investigation of photometric data and asteroids lightcurves. A particular solution of Euler-Liouville equation was found for an elongated symmetrical body. It may be useful for investigations of dual periods of rotational motion NPA tumbling asteroids. Physical formula of the gravity force moment acting at a rigid body was derived. A numerical solution of the same accurate equation was found and compared with the analytical ones. A stable region of the numerical solution was investigated and numerical algorithms for fast variables were examined. Very long time period of the numerical solution of Euler- Liouville equation for the body in gravitational field was found.