微扰Kepler系统的守恒量与对称性
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The conserved quantity and symmetry of perturbed kepler system
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    摘要:

    用直接积分法和Noether法研究微扰Kepler系统的守恒量,都得到了一个不同于Hamilton函数的守恒量,此守恒量与Runge-Lenz矢量有相同的量纲,可以称其为“类Runge-Lenz矢量守恒量”.文中还讨论了守恒量的Noether对称性、Lie对称性与Mei对称性,结果表明:与守恒量相应的无限小变换同时是Noether对称变换、Lie对称变换和Mei对称变换.

    Abstract:

    The conserved quantity of the perturbed Kepler system was studied by using the direct integral method and Noether method. One conserved quantity , different from the Hamiltonian, was obtained by two different methods .The dimension of the conserved quantity is identical with the RungeLenz vector's , so we can name this conserved quantity “analogous RungeLenz vector conserved quantity” . Furthermore, the Noether symmetry, the Lie symmetry and the Mei symmetry of the conserved quantity were also discussed. The research indicates that the infinitesimal transformations of the conserved quantity are all Noether symmetry, Lie symmetry and Mei symmetry.

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楼智美,葛伟宽.微扰Kepler系统的守恒量与对称性[J].动力学与控制学报,2009,7(4):313~317; Lou Zhimei, Ge Weikuan. The conserved quantity and symmetry of perturbed kepler system[J]. Journal of Dynamics and Control,2009,7(4):313-317.

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  • 收稿日期:2009-03-13
  • 最后修改日期:2009-04-11
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