Algorithm for numerical integration of the rigid-body equations of motion

Abstract

An algorithm for numerical integration of the rigid-body equations of motion is proposed. The algorithm uses the leapfrog scheme and the quantities involved are angular velocities and orientational variables that can be expressed in terms of either principal axes or quaternions. Due to specific features of the algorithm, orthonormality and unit norms of the orientational variables are integrals of motion, despite an approximate character of the produced trajectories. It is shown that the method presented appears to be the most efficient among all such algorithms known.