约束Hamilton系统的积分因子及其守恒量

The Integrating Factor and Conservation Quantity for Constrained Hamilton System

本文提出了约束Hamilton系统守恒量构成的一般途径.首先,给出了约束Hamilton系统的固有约束,并且建立了约束Hamilton系统正则方程;其次,给出了约束Hamilton系统的积分因子和守恒量定理;然后构建了约束Hamilton系统的广义Killing方程;最后举例说明其应用.显然,这种方法与之前的方法相比较,具有步骤清晰明了、限制条件少、运算简单的优点.

In this paper a general approach to constructing the conservation laws for constrained Hamilton system is presented. Firstly the internal constraint of the constrained Hamilton system is given and the canonical equation of the system is established. Secondly, the definition of integrating factors and the conservation theorem of constrained Hamilton system are given. Then the general Killing equation of the constrained Hamilton system is established. Finally, an example is given to illustrate the application of the integrating factor method. Obviously, compared with previous methods, this method has the advantages of clear calculation steps, less restrictive conditions and simple calculation.