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We introduce Spiral, a third-order integration algorithm for the rotationalmotion of extended bodies. It requires only one force calculation per timestep, does not require quaternion normalization at each time step, and can beformulated for both leapfrog and synchronous integration schemes, making itcompatible with many particle simulation codes. The stability and precision ofSpiral exceed those of state-of-the-art algorithms currently used in popularDEM codes such as Yade, MercuryDPM, LIGGGHTS, PFC, and more, at only slightlyhigher computational cost. Also, beyond DEM, we see potential applications inall numerical simulations that involve the 3D rotation of extended bodies.

SPIRAL: An Efficient Algorithm for the Integration of the Equation of Rotational Motion