刚体相互作用系统中转动运动积分的一种新方法
A new approach to the integration of rotational motion in systems with interacting rigid bodies
摘要：
本文提出了一种新的方法来数值积分相互作用刚性多原子分子系统的运动方程。借助蛙跳框架，我们直接将主角速度纳入积分，而定向位置则用主轴或四元数表示。结果表明，尽管对原子轨道进行了近似计算，但分子的刚性似乎是运动的积分。推导出的算法是免费的任何迭代程序，它允许执行节能和温度保存的模拟。相应的积分器是时间可逆的，但辛行为只是实现了平均。还描述了辛版本。在相空间中的体积精确地在每一个时间步长，而且，导致精确的解决方案，在惯性运动制度的角速度。结果表明，该算法具有良好的稳定性和保存的能量，甚至有点优于原子约束技术。
英文摘要：
A new approach is developed to integrate numerically the equations of motion for systems of interacting rigid polyatomic molecules. With the aid of a leapfrog framework, we directly involve principal angular velocities into the integration, whereas orientational positions are expressed in terms of either principal axes or quaternions. As a result, the rigidness of molecules appears to be an integral of motion, despite the atom trajectories are evaluated approximately. The algorithm derived is free of any iterative procedures and it allows to perform both energy- and temperature-conserving simulations. The corresponding integrators are time reversible but the symplectic behaviour is only achieved in mean. Symplectic versions are also described. The provide the conservation of volume in phase space precisely at each time step and, moreover, lead to exact solutions for angular velocities in the inertial-motion regime. It is shown that the algorithm exhibits excellent stability properties and conserves the energy even somewhat better than the atomic-constraint technique.
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