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Scientific paper
Jul 2005
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2005acasn..46..294l&link_type=abstract
Acta Astronomica Sinica, vol. 46, no. 3, p. 294-306
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2
Celestial Mechanics: Isolating Integral, Runge-Lenz Vector, Symplectic Method
Scientific paper
An intensive discussion is given here on an isolating integral and the trapezoidal rule applied to the preservation of the Runge-Lenz vector introduced by Minesaki and Nakamura. The isolating integral is an integral of a dynamical system which can further restrict the motion region of a particle in the system. It is well known that an integrable autonomous Hamiltonian system with n degrees of freedom must hold n independent isolating integrals in involution each other. If there exist other independent isolating integrals in this system, these isolating integrals have significance. It is clear that a bound Kepler problem contains energy integral, angular momentum integral and the Runge-Lenz vector. It is found that a symmetry group SO(3) formed by three independent isolating integrals in a dynamical system of two-dimensional Kepler motion is to be identified with a group of two-dimensional isotropic harmonic oscillator derived from the orginal Kepler system in terms of Levi-Civita transformation. As a result, the group of the isotropic harmonic oscillator can be strictly conserved by the trapezoidal rule. In addition, the trapezoidal rule can preserve exactly five orbital elements a, e, i, Ω and ω in a three-dimensional Kepler motion with five independent isolating integrals.
Liu Fu-Yao
Lu Ben-Ku
Wu Xiaolin
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