受微扰的二维各向同性谐振子系统的守恒量

Conserved quantityof Two-dimensional harmonic oscillator system by perturbation

采用扩展的P-S方法.首先,假定受微扰的二维各向同性谐振子系统存在守恒量;其次,分别用未知函数R,S去乘以恒为零的1-形式的微分式;然后,通过比较各系数求得未知函数R和S.由此求得了受微扰的二维各向同性谐振子系统的两守恒量I1和I2.研究并讨论了微扰系统守恒量的物理意义.结果表明,二维各向同性谐振子在受到微扰后,由于对称性的降低,其守恒量也发生了变化,在Lagrange体系中,其对称性与守恒量的关系可由Noether定理给出.

Extended Prelle-Singer method is used. This paper is based on the assumption that there are conserved quantities in two-dimensional harmonic oscillator system by perturbation, uses unknown functions R, S respectively to multiply a constant to zero 1-form style differential, and calculates coefficient R and S by comparing the integral multiplier. This paper discusses the physical significance of two conserved quantities. The results showed two-dimensional harmonic oscillator system by perturba- tion. Due to lower symmetry, the conserved quantity changed. In the Lagrange system, the relationship between symmetry and conserved quantities is given by Noether theorem.