Reliable event detection for Taylor methods in astrodynamics

21 Apr 2022  ·  Francesco Biscani, Dario Izzo ·

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.

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Earth and Planetary Astrophysics Instrumentation and Methods for Astrophysics Computational Engineering, Finance, and Science Computational Physics