Birkhoff系统的积分因子与守恒定理

Integrating Factors and Conservation Theorems for Birkhoffian Systems

本文提出了构造Birkhoff系统守恒律的积分因子方法。首先,给出了Birkkoff方程的积分因子的定义,研究了Birkhoff系统的守恒量存在必要条件;其次,建立了系统的积分因子与守恒律的对应关系,并给出了用于确定积分因子的广义Killing方程;最后,建立了守恒定理的逆定理。文末,举例说明结果的应用。

A general approach to the construction of conservation laws for Birkhoffian systems by finding corresponding integrating factors was presented. First, the definition of the integrating factors for Birkhoffian equations was given, and the necessary conditions for the existence of conserved quantities of Birkhoffian systems were studied in detail. Secondly, the relation between the conservation laws and the corresponding integrating factors was established,and the generalized Killing equations by which the integrating factors can be determinded were given. Finally, the inverse theorem of the conservation theorem for the systems was established. An example was given to illustrate the application of the results.