Simple, regular, and efficient numerical integration of rotational motion

Abstract

Among various formulations to integrate rotational motions numerically, we recommend the integration of the combination of Euler parameters and the angular velocity components referred to the body-fixed reference frame with the renormalization of the Euler parameters at every integration step. This is because the formulation proposed is not only simple and regular, but also stable and precise in studying rotational motions numerically. Its efficiency is not degraded even for almost uniform rotations if their nominal uniform part is separated by Encke's method. © 2008. The American Astronomical Society. All rights reserved.