广义Hamilton系统的Mei对称性导致的Mei守恒量

研究广义Hamilton系统的Mei对称性导致的守恒量. 首先,在群的一般无限小变换下给出广义Hamilton系统的Mei对称性的定义、判据和确定方程;其次,研究系统的Mei守恒量存在的条件和形式,得到Mei对称性直接导致的Mei守恒量; 而后,进一步给出带附加项的广义Hamilton系统Mei守恒量的存在定理; 最后,研究一类新的三维广义Hamilton系统,并研究三体问题中3个涡旋的平面运动. 关键词： 广义Hamilton系统 Mei对称性 Mei守恒量 三体问题

Mei symmetry leading to Mei conserved quantity of generalized Hamiltonian system

For a generalized Hamiltonian system, Mei conserved quantity derived by using Mei symmetry is studied. First, the definition,the criterion and the determining equations of Mei symmetry of generalized Hamiltonian system are given under infinitesimal transformations of group. Second, the conditions and the forms for existence of Mei conserved quantity are directly obtained by using the Mei symmetry of the system. Then, the theorem for existence of Mei conserved quantity of generalized Hamiltonian system with additional terms is given. Finally, a new three-dimensional generalized Hamiltonian system and the plane motion of the three vortices of three-body problem are studied by using the method presented in the paper.