论文标题
在时间转换的LeapFrog集成器上，椭圆和双曲线轨道上的逐步效果
Step-size effect in the time-transformed leapfrog integrator on elliptic and hyperbolic orbits
论文作者
论文摘要
已知已众所周知，用于时间转换的可分离性汉密尔顿（或时间转换的符号整合器； tsi）的漂移踢式跑步（DKD）类型leapfrog symblectic Integator已被应用于开头轨道。我们发现，对于椭圆轨道，该功能出现在任意步长。但是，双曲线轨道并非如此：当半步密大于平均异常的共轭力时段时，发生相变，新位置会跳到双曲线轨迹的非物理对应物。一旦发生，节能就会破裂。取而代之的是，动能减去势能成为一种新的保守量。我们为这种现象提供了数学解释。我们的结果提供了对TSI方法的更深入的理解，并且当使用TSI方法来解决双曲线相遇时，对步长的有用约束。当使用（Bulirsch-Stoer）外推积分子一起使用时，这一点特别重要，这需要集成误差的收敛性。
A drift-kick-drift (DKD) type leapfrog symplectic integrator applied for a time-transformed separable Hamiltonian (or time-transformed symplectic integrator; TSI) has been known to conserve the Kepler orbit exactly. We find that for an elliptic orbit, such feature appears for an arbitrary step size. But it is not the case for a hyperbolic orbit: when the half step size is larger than the conjugate momenta of the mean anomaly, a phase transition happens and the new position jumps to the nonphysical counterpart of the hyperbolic trajectory. Once it happens, the energy conservation is broken. Instead, the kinetic energy minus the potential energy becomes a new conserved quantity. We provide a mathematical explanation for such phenomenon. Our result provides a deeper understanding of the TSI method, and a useful constraint of the step size when the TSI method is used to solve the hyperbolic encounters. This is particular important when an (Bulirsch-Stoer) extrapolation integrator is used together, which requires the convergence of integration errors.
