Numerical Algorithms for Solving Restricted Three Body Problem

Abstract:

A precise integration algorithm for solving the restricted three body problem was put forward based on precise integration method, which divided a large integration time into small intervals and only small value matrix participates in the iterative process during the computation of the exponent matrix. And another symplectic algorithm for solving non-separable Hamiltonian system constructed by flow complex was also introduced, which only had periodic variational energy. The results of both algorithms were compared with fourth Runge-Kutta algorithm and their performances and advantages were analyzed, showing the validities of these two algorithms.

• Periodical: Applied Mechanics and Materials (Volumes 40-41)
• Pages: 917-923
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.40-41.917
• Online since: November 2010
• Authors: Yun Yan Zhang, Yan Jun Li, Nan Li
• Keywords: Hamiltonian System, Precise Integration, Restricted Three Body Problem, Symplectic Algorithm

References

[1] H. Yoshida: Physics Letter A Vol. 150 (1990), p.262–268.

[2] X.H. Liao, L. Liu: Progress in Astronomy Vol. 14 (1996), p.3–11.

[3] F.Y. Liu, X. Wu, B.K. Lu: ACTA Astronomica SINICA Vol 47 (2006), p.418–431.

[4] K. Feng, M.Z. Qin: Symplectic Geometric Algorithms for Hamiltonian Systems (Zhejiang Science and Technology Press, Zhejiang 2003).

[5] X.H. Liao, L. Liu: Chinese Journal of Computational Physics Vol. 12 (1995), p.102–108.

[6] K.C. Howell: Celestial Mechanics Vol. 32 (1984), pp.53-71.

[7] A. Jorba, J. Masdemont: Physica D Vol. 132 (1999), pp.189-213.

[8] W.X. Zhong: Symplectic Solution Mehtodology in Applied Mechanics (Higher Education Press, Beijing 2006).