Dynamically equivalent implicit algorithms for the integration of rigid body rotations

摘要

Two 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.