A new Lie symmetrical method of finding conserved quantity for Birkhoffian systems

作者：Li Zhuangjun; Luo Shaokai^*

来源：Nonlinear Dynamics, 2012, 70(2): 1117-1124.

DOI：10.1007/s11071-012-0517-9

• Birkhoffian system
• Lie group
• Lie symmetry
• Conserved quantity

For a Birkhoffian system, a new Lie symmetrical method to find a conserved quantity is given. Based on the invariance of the equations of motion for the system under a general infinitesimal transformation of Lie groups, the Lie symmetrical determining equations are obtained. Then, several important relationships which reveal the interior properties of the Birkhoffian system are given. By using these relationships, a new Lie symmetrical conservation law for the Birkhoffian system is presented. The new conserved quantity is constructed in terms of infinitesimal generators of the Lie symmetry and the system itself without solving the structural equation which may be very difficult to solve. Furthermore, several deductions are given in the special infinitesimal transformations and the results are reduced to a Hamiltonian system. Finally, one example is given to illustrate the method and results of the application.

• 出版日期2012-10
• 单位浙江理工大学