完整约束力学系统保Lie对称性差分格式

The Lie point symmetry-preserving difference scheme of holonomic constrained mechanical systems

提出一种保完整约束力学系统Lie点对称性的差分格式.其具体做法是:首先求出完整约束力学系统的Lie点对称群,并将其延拓到离散的差分格点上;其次利用其特征方程找出独立的离散不变量;再应用独立的离散不变量来构造不变量的差分格式,且此差分格式在连续极限下应给出原系统的微分方程;最后给出一个例子,作为本文结果的说明.

In this paper a Lie point symmetry- preserving difference schemes approximating holonomic constrained mechanical systems is presented. The procedure is as follows： Firstly we find the Lie point symmetry groups of the original equation, and prolong them to three points of the lattice. Secondly the discrete invariants are obtained by solving discrete characteristic equations,then the invariant difference scheme is constructed by using these discrete invariants; and this invariants difference scheme will give the original equation under the continuous limit. Finally an example is presented to illustrate the applications of the result.