Quaternion-based rigid body rotation integration algorithms for use in particle methods

The resolution of translational motion in discrete element method and molecular dynamics applications is a straightforward task; however, resolving rotational motion is less obvious. Many applications update rotation using an explicit integration involving products of matrices, which has well-known drawbacks. Although rigid body rotation has received attention in large-angle rotation applications, relatively little attention has been dedicated to the unique requirements of particle methods using explicit time-stepping algorithms. This paper reviews existing explicit algorithms and shows the benefits of using a quaternion-based re-parameterization of both the central difference algorithm and the approach of Munjiza et al. (Int. J. Numer. Meth. Engng 2003; 56:36–55). The improvement not only provides guaranteed orthonormality of the resulting rotation but also allows the assumption of small-angle rotation to be relaxed and the use of a more accurate Taylor expansion instead. The current and quaternion-based algorithms are compared for accuracy and computational efficiency. Copyright © 2007 John Wiley & Sons, Ltd.