广义Hamilton系统的一类不变性与守恒量

Invariance and Conserved Quantity of the Generalized Hamilton System

用无限小变换的方法,研究广义Hamilton系统在时间和坐标的无限小变换下的一种新的不变性,并由这种不变性导出一类守恒量的存在条件和形式,给出寻找守恒量的一类新方法.用典型例子说明方法的应用.结果表明,该方法不同于Noether方法、Lie方法及形式不变性方法.

Using the method of infinitesimal transformations, a new invariance of the generalized Hamilton system under infinitesimal transformations of time and coordinates is studied. From this the conditions and forms of existence of a conserved quantity of the system are derived. A new method to seek the conserved quantity is given. Some typical examples are given to illustrate the application of the method. The results indicate that the method is different from the Noether method, the Lie method and the form invariance method.