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二维各向异性谐振子和两分振子的能量是守恒的, 但三个守恒量中只有其中两个是独立的. 当频率比1/2 为有理数时, 系统存在第三个独立的守恒量.本文用扩展Prelle-Singer 法得到五个典型谐振子的第三个独立守恒量, 并讨论了与守恒量相应的Noether对称性与Lie对称性.
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关键词:
- 扩展Prelle-Singer法/
- 二维各向异性谐振子/
- 守恒量/
- 对称性
The energy and the two partial energies of two-dimensional anisotropic harmonic oscillator are conserved quantities, but only two of them are independent. The system possesses the third independent conserved quantity when the 1/2 is a rational number. The extended Prelle-Singer method is used to find the third independent conserved quantity for the five typical two-dimensional anisotropic harmonic oscillators. The Noether symmetry and the Lie symmetry of the third independent conserved quantities are also discussed.-
Keywords:
- extended P-S method/
- two-dimensional anisotropic harmonic oscillator/
- conserved quantity/
- symmetry
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