非保守力和非完整约束对Hamilton系统Noether对称性的影响(英文)

Effects of Non-conservative Forces and Nonholonomic Constraints on Noether Symmetries of a Hamilton System

研究非保守力和非完整约束对Hamilton系统的Noether对称性的影响。Hamilton系统受到非保守力或非完整约束作用时,系统的Noether对称性和守恒量都会发生变化。原有的一些Noether对称性消失了,一些新的Noether对称性产生了,在一定条件下,一些Noether对称性仍保持不变。文中分别给出了系统的Noether对称性以及守恒量保持不变的条件,并举例说明结果的应用。

The effects of non-conservative forces and nonholonomic constraints on Noether symmetries and conserved quantities of a Hamilton system are studied. When non-conservative forces or nonholonomic constraints are exerted on a Hamilton system,the Noether symmetries and the conserved quantities of the system may vary. It can be seen that some Noether symmetries disappear,some new Noether symmetries emerge,and under certain conditions some Noether symmetries will still remain. In this paper,the conditions under which the Noether symmetries and the conserved quantities of the system will remain are respectively obtained,and two examples are given to illustrate the application of the results.