提出了用泊松括号求一阶近似守恒量的方法，将微扰力学系统的Hamilton函数看成是未受微扰作用系统的Hamilton函数和微扰项两部分组成.先根据未受微扰作用力学系统的特点选择一种合适的方法求得其精确守恒量，再利用泊松括号和偏微分方程的性质求得守恒量的一阶微扰项，最后根据Noether对称性、Lie对称性和Mei对称性性质，求得与一阶近似守恒量相应的一阶近似Noether对称性、近似Lie对称性和近似Mei对称性.研究了受微扰作用的二维各向同性谐振子的一阶近似守恒量和近似对称性，得到了系统的3个一阶近似守恒量及它们相应的一阶近似对称性.结果表明，与3个一阶近似守恒量相应的一阶近似对称性既是近似Noether对称性，又是近似Lie对称性，也是近似Mei对称性.
A Poisson bracket method to obtain the first order approximate conserved quantities of two-dimensional perturbed mechanical system is proposed. We consider the perturbed Hamiltonian function as the combination of Hamiltonian function of unperturbed system and the perturbed term. First, according to the peculiarity of unperturbed system, we select a suitable method to obtain the exact conserved quantities of unperturbed system. Second, we calculate the first order perturbed terms of conserved quantities by using Poisson bracket and the character of partial differential equations. Finally, according to the characters of Noether symmetries, Lie symmetries and Mei symmetries, the first order approximate Noether symmetries, approximate Lie symmetries and approximate Mei symmetries of the first order approximate conserved quantities can be obtained. A perturbed two-dimensional isotropic harmonic oscillator is studied in this paper, and three first order approximate conserved quantities are obtained by using Poisson bracket method, and the first order approximate symmetries of three first order approximate conserved quantities are either approximate Noether symmetries or approximate Lie symmetries and Mei symmetries.
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