相空间中含时滞的非保守力学系统的Noether定理

研究相空间中含时滞的非保守力学系统的Noether对称性与守恒量。建立含时滞的非保守系统动力学的Hamilton正则方程;依据相空间中含时滞的Hamilton作用量在无限小群变换下的广义准不变性,给出相空间中含时滞的Noether广义准对称变换的定义和判据;并建立相空间中含时滞的非保守力学系统的Noether对称性与守恒量之间的联系。文末,举例说明结果的应用。

Noether Theorem for Nonconservative Mechanical System with Time Delay in Phase Space

The Noether symmetries and the conserved quantities for nonconservative mechanical systems with time delay in phase space are studied. Firstly, the Hamilton canonical equations with time delays for the non-conservative systems are established. Secondly, according to the generalized quasi-invariance of the Hamilton action with time delay in phase space under the infinitesimal transformations of groups, the definitions and criterion of the Noether generalized quasi symmetric transformations with time delay in phase space are given. Lastly, the relationship between the Noether symmetries and the conserved quantities with time delay in phase space are established. At the end, an example is given to illustrate the application of the results.