标题： 螺旋：旋转运动方程积分的高效算法 显示英文标题

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

摘要： 我们介绍Spiral，这是一种用于扩展体旋转运动的三阶积分算法。它每一步时间只需要一次力计算，不需要在每一步时间进行四元数归一化，并且可以为跳跃蛙和同步积分方案进行公式化，使其与许多粒子模拟代码兼容。Spiral的稳定性和精度优于目前在流行DEM代码如Yade、MercuryDPM、LIGGGHTS、PFC等中使用的最先进算法，仅带来稍高的计算成本。此外，除了DEM之外，我们还看到在涉及扩展体三维旋转的所有数值模拟中都有潜在的应用。 显示英文摘要

摘要： We introduce Spiral, a third-order integration algorithm for the rotational motion of extended bodies. It requires only one force calculation per time step, does not require quaternion normalization at each time step, and can be formulated for both leapfrog and synchronous integration schemes, making it compatible with many particle simulation codes. The stability and precision of Spiral exceed those of state-of-the-art algorithms currently used in popular DEM codes such as Yade, MercuryDPM, LIGGGHTS, PFC, and more, at only slightly higher computational cost. Also, beyond DEM, we see potential applications in all numerical simulations that involve the 3D rotation of extended bodies.