Dynamically equivalent implicit algorithms for the integration of rigid body rotations

Abstract

AbstractTwo midpoint‐trapezoid pairs of dynamically equivalent (conjugate) algorithms are derived as compositions of first‐order forward Euler and backward Euler integrators as applied to an incremental form of the initial‐value problem of three‐dimensional rigid body rotation. The algorithms are related to the recently developed methodology of the so‐called Munthe‐Kaas Runge–Kutta methods. Selected examples are used to illustrate the excellent long‐term integration properties. Copyright © 2006 John Wiley & Sons, Ltd.