Abstract:

This paper researches the effection of symmetry reduction to the numerical integration for holonomic system. Through numerical experiment, there is not essential effection for numerical integrator when system is reduced to lower dimension. But under the reduced system, it can effectively decrease the difficulty of writing program and the time of computation. So for the complicated dynamical system, it should be firstly reduced by symmetry methods and obtain the dynamical system with less degree of freedom, then the dynamical nature of system can be researched under the reduced system.

Key words: holonomic system, symmetry reduction, numerical integration

摘要：

研究对称约化对完整系统数值积分的影响。通过数值实验发现, 对称约化对完整系统的数值积分结果没有本质的影响, 但是在约化后的系统下进行数值积分可以有效地减少程序编写的难度和计算时间。对于复杂的动力学系统, 可以先对其进行对称约化, 以获得较少自由度的动力学系统, 然后在约化系统下进行数值计算, 间接地研究原系统的动力学性质。

关键词: 完整系统, 对称约化, 数值积分