应用三阶力梯度辛算法求解纯Kepler二体问题

Application of third-order force-gradient symplectic algorithms to the pure Keplerian two-body problem

针对可分解为动能T部分和势能V部分的哈密顿系统,本文构造了六个三阶力梯度辛算法,并应用它们求解纯Kepler二体问题的轨道长半径,相对误差结果显示了其有效性。这些辛算法因具有保持能量和辛结构的优点已经成为研究Hamilton系统长期定性演化的最佳工具。

In this paper,we construct six new third-order force-gradient symplectic algorithms for the natural splitting of a Hamiltonian system into kinetic energy and potential energy. For the semimajor axis of a pure Keplerian two-body problem,they are both effective in the accuracy of the relative error. Preserving the symplectic structure and giving no secular change in energy errors,it has been an ideal tool for studying the long-term dynamical evolution.