Spectrol properties of symplectic integrators for problem on motion of a free rigid body

Abstract

In this paper a new approach useful for numerical integration of the motion equations for a free rigid body with a fixed point is studied. The approach employs symplectic integration schemes of the second and third order. These schemes are presented as a sequence of rotations with two frequencies per each integration step. Roth schemes are implemented and tested against Runge-Kutta-Fehlberg fifth order method, the represented computational results are satisfactory.