研究Noether准对称性定理的时间重新参数化方法

The time-reparameterization method for Noether's quasi-symmetry theorems

提出并建立了证明Noether准对称性与守恒量定理的时间重新参数化方法。首先,在时间不变的无限小变换群下给出Lagrange系统和Hamilton系统的Noether准对称性定理;其次,利用时间重新参数化方法给出在时间变化的一般无限小变换群下Lagrange系统和Hamilton系统的Noether准对称性定理。最后,举例说明结果的应用。

The time-reparameterization method was proposed and applied to prove Noether＇s theorems of quasi- symmetry and conserved quantity. Firstly, based on the infinitesimal group of transformations without transforming time, Noether,s quasi -symmetry theorems for Lagrange system and Hamilton system were given. Secondly, Noether＇s quasi-symmetry theorems for Lagrange system and Hamilton system under the general infinitesimal group of transformations with transforming time were given by using the time-reparameterization method. Finally, two examples were provided to illustrate the application of the results.