van Zon Ramses, Schofield Jeremy
Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario, Canada M5S 3H6.
Phys Rev E Stat Nonlin Soft Matter Phys. 2007 May;75(5 Pt 2):056701. doi: 10.1103/PhysRevE.75.056701. Epub 2007 May 3.
Elegant integration schemes of second and fourth order for simulations of rigid-body systems are presented which treat translational and rotational motion on the same footing. This is made possible by a recent implementation of the exact solution of free rigid-body motion. The two schemes are time reversible and symplectic, and exactly respect conservation principles for both the total linear and the angular momentum vectors. Simulations of simple test systems show that the second-order scheme is stable and conserves all constants of the motion to high precision. Furthermore, the schemes are demonstrated to be more accurate and efficient than existing methods, except for high densities, in which case the second-order scheme performs at least as well, showing their general applicability. Finally, it is demonstrated that the fourth-order scheme is more efficient than the second-order scheme provided the time step is smaller than a system-dependent threshold value.
提出了用于刚体系统模拟的二阶和四阶优雅积分方案，该方案在相同基础上处理平移和旋转运动。这是通过最近对自由刚体运动精确解的实现得以实现的。这两种方案是时间可逆且辛的，并且精确地遵循总线性动量和角动量矢量的守恒原理。简单测试系统的模拟表明，二阶方案是稳定的，并且能高精度地守恒所有运动常数。此外，除了在高密度情况下二阶方案至少表现得一样好之外，这些方案被证明比现有方法更准确、更高效，显示了它们的普遍适用性。最后，证明了只要时间步长小于一个与系统相关的阈值，四阶方案就比二阶方案更高效。
