We present WHFast, a fast and accurate implementation of a Wisdom-Holman symplectic integrator for long-term orbit integrations of planetary systems. WHFast is significantly faster and conserves energy better than all other Wisdom-Holman integrators tested. We achieve this by significantly improving the Kepler-solver and ensuring numerical stability of coordinate transformations to and from Jacobi coordinates. These refinements allow us to remove the linear secular trend in the energy error that is present in other implementations. For small enough timesteps we achieve Brouwer's law, i.e. the energy error is dominated by an unbiased random walk due to floating-point round-off errors. We implement symplectic correctors up to order eleven that significantly reduce the energy error. We also implement a symplectic tangent map for the variational equations. This allows us to efficiently calculate two widely used chaos indicators the Lyapunov characteristic number (LCN) and the Mean Exponential Growth factor of Nearby Orbits (MEGNO). WHFast is freely available as a flexible C package, as a shared library, and as an easy-to-use python module.
翻译:我们展示了WHFAST, 快速和准确地实施了行星系统长期轨道整合的Wisdom-Holman共生综合体。WHFAST比其他所有经过测试的Wisdom-Holman共生体要快得多,保存的能源也比其他所有经过Wisdom-Holman共生体测试的Wisdom-Holman共生体要快得多。我们通过大大改进开普勒-开关和确保协调转换与Jacobi坐标的数值稳定,实现了这一点。这些改进使我们能够消除其他执行中存在的能源错误中的线性长期性趋势。对于足够小的时间步骤来说,我们达到了Brouwer的法律,即能源错误以无偏见的随机行走为主。我们实施了静无偏的节能纠正器,以11号为主,大大降低了能源误差。我们还为变异方方方形配置了一个静脉色图。这使我们能够有效地计算出两种广泛使用的混乱指标:Lyapunov 特征(LCN) 和近比轨道(MEGEPentententent Estare Grows) 的偏差增长系数(MEGEG), as-Wy-s-s- as-s-s-s- as-ly-ly-lytototo asto alylylyly as-ly lipliply-pliply-ply-p-ply-ly-p-ly-ply-ly-ly-ly-ly-p-ly-ly-ly-ly-ply-ly-ly-ly-ly-ly-ly-ly-ly-ly-ly-ly-ly-ly-ly-ly-ly-ly-ly-ly-ly-ly-ly-ly-ly-ly-ly-ly-p-ly-ly-ly-ly-ly-ly-ly-ly-ly-ly-ly-ly-ly-ly-ly-ly-ly-ly-ly-ly-ly-ly-ly-ly-ly-ly-ly-ly-ly-ly-ly-ly-ly-ly-ly-ly-ly-ly-ly-ly-ply-ly-ly-ly-ly-ly-ly-ly-p