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.