论文标题
泰勒方法的可靠事件检测
Reliable event detection for Taylor methods in astrodynamics
论文作者
论文摘要
我们提出了一种新的方法，用于检测普通微分方程系统中的事件。新方法将泰勒集成剂的独特特征与最先进的多项式根找到技术结合在一起，以产生一种新型算法，以确保在适度的计算开销中确保强大的事件检测保证。详细的测试和基准，重点介绍了天体动力学和天体力学问题（例如碰撞N型系统，围绕不规则身体的航天器动力学考虑到蚀的腹膜，计算Poincare的“ poincare”部分等）显示了我们的方法在绩效和策略中如何在现代数字集成工作中使用策略，在现代数字集成工作中采用的策略是如何卓越的。新算法可在我们的开源Taylor Integration Package Heyoka中找到。
We present a novel approach for the detection of events in systems of ordinary differential equations. The new method combines the unique features of Taylor integrators with state-of-the-art polynomial root finding techniques to yield a novel algorithm ensuring strong event detection guarantees at a modest computational overhead. Detailed tests and benchmarks focused on problems in astrodynamics and celestial mechanics (such as collisional N-body systems, spacecraft dynamics around irregular bodies accounting for eclipses, computation of Poincare' sections, etc.) show how our approach is superior in both performance and detection accuracy to strategies commonly employed in modern numerical integration works. The new algorithm is available in our open source Taylor integration package heyoka.
