标题： 用于少体系统积分的可逆时间步长适应 显示英文标题

标题： Reversible time-step adaptation for the integration of few-body systems

摘要： 时间步长准则在直接N体代码中起着关键作用。如果不谨慎选择，会导致能量误差的长期漂移。共享自适应时间步长准则通常采用最小的成对时间步长，这在时间步长的时间演化中存在不连续性。这对时间步长对称化算法的运行有较大影响。我们提供了对先前发现的新演示，即在N体系统中对所有成对时间步长进行平滑加权平均，可以提高能量守恒的水平。此外，我们通过考虑3种加权时间步长的方法和9种对称化方法，比较了27种不同的时间步长准则的性能。我们对强混沌的少体系统进行了性能测试，包括不稳定的三体系统、共振链中的大行星以及当前的太阳系。我们发现谐波对称化方法（在我们的符号中为方法A3和B3）最为稳健，即对称化的时间步长仍接近时间步长函数。此外，基于我们的太阳系实验，我们发现基于直接成对平均的新加权方法（在我们的符号中为方法W2），比其他方法略有优势。 显示英文摘要

摘要： The time step criterion plays a crucial role in direct N-body codes. If not chosen carefully, it will cause a secular drift in the energy error. Shared, adaptive time step criteria commonly adopt the minimum pairwise time step, which suffers from discontinuities in the time evolution of the time step. This has a large impact on the functioning of time step symmetrisation algorithms. We provide new demonstrations of previous findings that a smooth and weighted average over all pairwise time steps in the N-body system, improves the level of energy conservation. Furthermore, we compare the performance of 27 different time step criteria, by considering 3 methods for weighting time steps and 9 symmetrisation methods. We present performance tests for strongly chaotic few-body systems, including unstable triples, giant planets in a resonant chain, and the current Solar System. We find that the harmonic symmetrisation methods (methods A3 and B3 in our notation) are the most robust, in the sense that the symmetrised time step remains close to the time step function. Furthermore, based on our Solar System experiment, we find that our new weighting method based on direct pairwise averaging (method W2 in our notation), is slightly preferred over the other methods.