相空间中变质量力学系统Lie-Mei对称性的两个守恒量

研究相空间中变质量力学系统Lie-Mei对称性导致的两个守恒量，给出系统Lie-Mei对称性的定义和判据，引入谐调函数，得到系统Lie-Mei对称性导致的两个守恒量的条件和形式，并给出应用算例. 由于谐调函数可根据寻找规范函数的需要适当选取，且选取具有多样性，因此能够找到系统Lie-Mei对称性更多的守恒量. 关键词： 相空间 变质量系统 Lie-Mei对称性 守恒量

Two types of conserved quantities of Lie-Mei symmetry for a variable mass system in phase space

Two types of conserved quantities deduced by Lie-Mei symmetry of variable mass mechanical system are studied in phase space in the paper. The definition and criterion of Lie-Mei symmetry for the system are given. A coordination function is introduced，and the conditions under which the Lie-Mei symmetry leads to the two types of conserved quantities and the forms of the two types of conserved quantities are obtained. An illustrative example is given. The coordination function can be selected according to the requirement for finding the gauge function，and the choice of the coordination function is multiformal，so more conserved quantities can be deduced from Lie-Mei symmetry of the system.