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

作者：Su, Xiang-Ning; Wu, Xin^*; Liu, Fu-Yao

来源：Astrophysics and Space Science, 2016, 361(1): 32.

DOI：10.1007/s10509-015-2614-y

• Celestial mechanics
• Symplectic integrator
• Circular restricted three-body problem
• Chaos

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.

• 出版日期2016-1
• 单位上海立信会计金融学院; 南昌大学