NON-EXISTENCE OF THE MODIFIED FIRST INTEGRAL BY SYMPLECTIC INTEGRATION METHODS II: KEPLER PROBLEM

机译：辛积分方法修正的第一积分的不存在II：开普勒问题

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Symplectic integration methods conserve the Hamiltonian quite well because of the existence of the modified Hamiltonian as a formal conserved quantity. For a first integral of a given Hamiltonian system, the modified first integral is defined to be a formal first integral for the modified Hamiltonian. It is shown that the Runge-Lenz vector of the Kepler problem is not well conserved by symplectic methods, and that the corresponding modified first integral does not exist. This conclusion is given for a one-parameter family of symplectic methods including the symplectic Euler method and the Stoermer/Verlet method.

机译：辛积分方法很好地保存了哈密顿量，因为存在修正的哈密顿量作为形式守恒量。对于给定哈密顿系统的第一积分，修改后的第一积分定义为修改后的哈密顿量的形式第一积分。证明了开普勒问题的Runge-Lenz向量不能用辛方法很好地守恒，并且相应的修正第一积分不存在。对于单参数辛方法，包括辛欧拉方法和Stoermer / Verlet方法，给出了这一结论。

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来源
《Third Meeting on Celestical Mechanics - CELMEC III Jun 18-22, 2001 Rome, Italy》|2001年|p.355-364|共10页
会议地点 Rome(IT);Rome(IT)
作者
HARUO YOSHIDA;
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作者单位

National Astronomical Observatory of Japan, Mitaka, Tokyo 181 -8588, Japan;

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会议组织
原文格式 PDF
正文语种 eng
中图分类天文学;
关键词
symplectic integration method; modified hamiltonian; modified first integral; kepler problem; runge-lenz vector;

机译：辛积分法;修正的哈密顿量;修正的第一积分;开普勒问题;龙格-伦兹向量;

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NON-EXISTENCE OF THE MODIFIED FIRST INTEGRAL BY SYMPLECTIC INTEGRATION METHODS II: KEPLER PROBLEM

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