SYMPLECTIC INTEGRATION OF HAMILTONIAN-SYSTEMS
SYMPLECTIC INTEGRATION OF HAMILTONIAN-SYSTEMS
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DOI：
10.1088/0951-7715/3/2/001
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发表时间：
1990-05-01
期刊：
影响因子：
1.7
通讯作者：
SCOVEL, C
中科院分区：
文献类型：
--
作者：
CHANNELL, PJ;SCOVEL, C
作者回顾了过去的工作，并提出了新的算法来数值积分哈密顿动力系统的轨迹。这些算法完全保留了辛2型，即保留了所有庞加莱不变量。这些算法已经在各种实例上进行了测试，并给出了Fermi-Pasta-Ulam非线性弦、Henon-Heiles系统、四涡问题和常负曲率流形上的测地流的结果。在所有情况下，算法都具有长期稳定性，并在相空间中保持全局几何结构。
The authors survey past work and present new algorithms to numerically integrate the trajectories of Hamiltonian dynamical systems. These algorithms exactly preserve the symplectic 2-form, ie they preserve all the Poincare invariants. The algorithms have been tested on a variety of examples and results are presented for the Fermi-Pasta-Ulam nonlinear string, the Henon-Heiles system, a four-vortex problem, and the geodesic flow on a manifold of constant negative curvature. In all cases the algorithms possess long-time stability and preserve global geometrical structures in phase space.