Reliable event detection for Taylor methods in astrodynamics

TL;DR

This paper introduces a new event detection algorithm for Taylor integrators that improves accuracy and performance in astrodynamics simulations by combining polynomial root finding with Taylor methods.

Contribution

The paper presents a novel event detection algorithm that guarantees strong detection accuracy with modest computational overhead, specifically tailored for Taylor integrators in astrodynamics.

Findings

Superior detection accuracy over existing methods

Enhanced performance in astrodynamics simulations

Effective handling of complex celestial mechanics problems

Abstract

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.