论文标题
层次多系统的世俗动力学由嵌套二进制组成，具有任意数量的身体和任意分层结构。 iii。亚轨道效应：混合整合技术和轨道校正
Secular dynamics of hierarchical multiple systems composed of nested binaries, with an arbitrary number of bodies and arbitrary hierarchical structure. III. Suborbital effects: hybrid integration techniques and orbit-averaging corrections
论文作者
论文摘要
世俗化代码在本系列的前两篇论文中介绍，将多个系统的长期动态演变与任何数量的物体和分层结构集成在一起，但前提是该系统由嵌套二进制文件组成。在形式主义的根本性上，我们以前在系统中的所有轨道上进行平均。这种近似显着加快了运动方程的数值整合，从而使大种群合成研究成为可能。但是，当系统的世俗演化时间尺度与系统中的任何一个轨道时期相比，平均近似值的轨道可能会分解。在这里，我们提出了对世俗化的更新，其中我们结合了混合整合技术和轨道平均校正。通过此更新，用户可以直接集成哪些轨道（无需平均）或假设轨道。对于直接集成的轨道，我们实施了两种集成技术，一种基于元素形式的运动运动方程式基于正规化的Kustaanheimo-Stiefel方程。我们还实施了分析轨道的校正，以实现成对相互作用到四极顺序的校正。此处介绍的更新为整合层次多系统的长期动力学演变提供了更大的灵活性。通过有效地结合直接集成和绕绕长期演化的绕，可以准确计算，但与现有直接N体代码相比，计算成本明显降低。我们提供了许多新功能有益的示例。我们的更新的代码可免费提供，该代码用C ++编写，并在Python中补充了用户友好的界面。
The SecularMultiple code, presented in two previous papers of this series, integrates the long-term dynamical evolution of multiple systems with any number of bodies and hierarchical structure, provided that the system is composed of nested binaries. In the formalism underlying SecularMultiple, we previously averaged over all orbits in the system. This approximation significantly speeds up numerical integration of the equations of motion, making large population synthesis studies possible. However, the orbit averaging approximation can break down when the secular evolution timescale of the system is comparable to or shorter than any of the orbital periods in the system. Here, we present an update to SecularMultiple in which we incorporate hybrid integration techniques, and orbit-averaging corrections. With this update, the user can specify which orbits should be integrated directly (without averaging), or assuming averaged orbits. For orbits that are integrated directly, we implemented two integration techniques, one which is based on the regularised Kustaanheimo-Stiefel equations of motion in element form. We also implemented analytical orbit-averaging corrections for pairwise interactions to quadrupole order. The updates presented here provide more flexibility for integrating the long-term dynamical evolution of hierarchical multiple systems. By effectively combining direct integration and orbit averaging the long-term evolution can be accurately computed, but with significantly lower computational cost compared to existing direct N-body codes. We give a number of examples in which the new features are beneficial. Our updated code, which is written in C++ supplemented with a user-friendly interface in Python, is freely available.
