Application of the logarithmic Hamiltonian algorithm to the circular restricted three-body problem with some post-Newtonian terms

详细信息    查看全文

• 作者：Xiang-Ning Su ; Xin Wu ; Fu-Yao Liu
• 关键词：Celestial mechanics ; Symplectic integrator ; Circular restricted three ; body problem ; Chaos
• 刊名：Astrophysics and Space Science
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：361
• 期：1
• 全文大小：1,465 KB
• 参考文献：Chandrasekhar, S., Contopoulos, G.: Proc. R. Soc. A 298, 123 (1967) CrossRef ADS MATH
  Emel’yanenko, V.V.: Celest. Mech. Dyn. Astron. 98, 191 (2007) MathSciNet CrossRef ADS MATH
  Forest, E., Ruth, R.D.: Physica D 43, 105 (1990) MathSciNet CrossRef ADS MATH
  Froeschlé, C., Lega, E.: Celest. Mech. Dyn. Astron. 78, 167 (2000) CrossRef ADS MATH
  Huang, G., Wu, X.: Phys. Rev. D 89, 124034 (2014a) CrossRef ADS
  Huang, G., Wu, X.: Gen. Relativ. Gravit. 46, 1798 (2014b) CrossRef ADS
  Maindl, T.I., Dvorak, R.: Astron. Astrophys. 290, 335 (1994) ADS
  Mei, L., Ju, M., Wu, X., Liu, S.: Mon. Not. R. Astron. Soc. 435, 2246 (2013a) CrossRef ADS
  Mei, L., Wu, X., Liu, F.: Eur. Phys. J. C 73, 2413 (2013b) CrossRef ADS
  Mikkola, S.: Celest. Mech. Dyn. Astron. 67, 145 (1997) MathSciNet CrossRef ADS MATH
  Mikkola, S., Aarseth, S.: Celest. Mech. Dyn. Astron. 84, 343 (2002) MathSciNet CrossRef ADS MATH
  Mikkola, S., Tanikawa, K.: Celest. Mech. Dyn. Astron. 74, 287 (1999) CrossRef ADS MATH
  Mikkola, S., Tanikawa, K.: New Astron. 20, 38 (2013) CrossRef ADS
  Ni, S., Wu, X.: Res. Astron. Astrophys. 14, 1329 (2014) CrossRef ADS
  Preto, M., Tremaine, S.: Astron. J. 118, 2532 (1999) CrossRef ADS
  Szebehely, V.: Theory of Orbits: The Restricted Problem of Three Bodies. Academic Press, New York (1967)
  Wang, H., Huang, G.Q.: Commun. Theor. Phys. 64, 159 (2015) CrossRef ADS
  Wu, X., Huang, T.Y.: Phys. Lett. A 313, 77 (2003) MathSciNet CrossRef ADS MATH
  Wu, X., Huang, G.: Mon. Not. R. Astron. Soc. 452, 3167 (2015) CrossRef ADS
  Wu, X., Huang, T.Y., Zhang, H.: Phys. Rev. D 74, 083001 (2006) MathSciNet CrossRef ADS
  Wu, X., Mei, L., Huang, G., Liu, S.: Phys. Rev. D 91, 024042 (2015) CrossRef ADS
  Yoshida, H.: Phys. Lett. A 150, 262 (1990) MathSciNet CrossRef ADS
  Zhong, S.Y., Wu, X., Liu, S.Q., Deng, X.F.: Phys. Rev. D 82, 124040 (2010) CrossRef ADS
  
• 作者单位：Xiang-Ning Su (1)
  Xin Wu (1)
  Fu-Yao Liu (2)
  
  1. Department of Physics & Institute of Astronomy, Nanchang University, Nanchang, 330031, China
  2. School of Mathematics and Information, Shanghai Lixin University of Commerce, Shanghai, 201600, China
  
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Astronomy
  
• 出版者：Springer Netherlands
• ISSN：1572-946X

文摘

An implementation of a fourth-order symplectic algorithm to the logarithmic Hamiltonian of the Newtonian circular restricted three-body problem in an inertial frame is detailed. The logarithmic Hamiltonian algorithm produces highly accurate results, comparable to the non-logarithmic one. Its numerical performance is independent of an orbital eccentricity. However, it is not when some post-Newtonian terms are included in this problem. Although the numerical accuracy becomes somewhat poorer as the orbital eccentricity gets larger, it is still much higher than that of the non-logarithmic Hamiltonian algorithm. As a result, the present code can drastically eliminate the overestimation of Lyapunov exponents and the spurious rapid growth of fast Lyapunov indicators for high-eccentricity orbits in the Newtonian or post-Newtonian circular restricted three-body problem.