A new Lie symmetrical method of finding a conserved quantity for a dynamical system in phase space

作者：Luo Shao Kai^*; Li Zhuang Jun; Li Lin

来源：Acta Mechanica, 2012, 223(12): 2621-2632.

DOI：10.1007/s00707-012-0729-6

For a dynamical system in phase space, a new Lie symmetrical method to find a conserved quantity is presented in a general infinitesimal transformation of Lie groups. Based on the invariance of the differential equations of motion for the system under a general infinitesimal transformation of Lie groups, the Lie symmetrical determining equations are obtained. Then, an important relationship that reveals the interior properties of a dynamical system in phase space is given. By using the relationship, a Lie symmetrical basic integral variable relation and a new Lie symmetrical conservation law for the dynamical system in phase space are given. The new conserved quantity is constructed in terms of the infinitesimal generators of Lie symmetry and the system itself without solving the structural equation. Furthermore, the method is applied in the Hamiltonian system, the nonconservative Hamiltonian system and the nonholonomic Hamiltonian system. Finally, one example is given to illustrate the method and results of the application.

• 出版日期2012-12
• 单位浙江理工大学