用扩展的力梯度辛方法研究旋转星系中的混沌
Study of chaos in rotating galaxies using extended force-gradient symplectic methods
摘要：
我们考虑到三种类型的模型的旋转星系在极坐标系中的旋转框架的动力学。由于非轴对称位扰动，角动量随时间变化，动能取决于动量和空间坐标。现有的显式力梯度辛积分不适用于这样的哈密顿问题，但最近提出的扩展力梯度辛方法在以前的工作。数值比较表明，具有对称性的扩展力梯度四阶辛方法在精度上优于标准四阶辛方法，但不如优化的扩展力梯度四阶辛方法.利用对称性优化的扩展算法研究了这些旋转星系模型中规则轨道和混沌轨道的动力学特征。引力效应和混沌度随势级数展开式中径向项数目的增加而增加。在级数展开式、能量和初始条件的径向项数目相同的情况下，三类模型的正则轨道和混沌轨道具有相似的动力学结构。
英文摘要：
We take into account the dynamics of three types of models of rotating galaxies in polar coordinates in a rotating frame. Due to non-axisymmetric potential perturbations, the angular momentum varies with time, and the kinetic energy depends on the momenta and spatial coordinate. The existing explicit force-gradient symplectic integrators are not applicable to such Hamiltonian problems, but the recently extended force-gradient symplectic methods proposed in a previous work are. Numerical comparisons show that the extended force-gradient fourth-order symplectic method with symmetry is superior to the standard fourth-order symplectic method but inferior to the optimized extended force-gradient fourth-order symplectic method in accuracy. The optimized extended algorithm with symmetry is used to explore the dynamical features of regular and chaotic orbits in these rotating galaxy models. The gravity effects and the degree of chaos increase with an increase of the number of the radial terms in the series expansions of the potential. There are similar dynamical structures of regular and chaotical orbits in the three types of models for the same number of the radial terms in the series expansions, energy and initial conditions.
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