Stable sets mapping with Taylor differential algebra with application to ballistic capture orbits around Mars

TL;DR

This paper introduces a novel algorithm using Taylor differential algebra for efficiently identifying ballistic capture orbits around Mars, significantly reducing computational effort compared to traditional grid sampling methods.

Contribution

The work presents a new continuous search space mapping algorithm based on Taylor differential algebra, improving efficiency and accuracy in finding ballistic capture orbits around Mars.

Findings

Over 87% of the search space is guaranteed accurate.

The algorithm effectively captures dynamical variations across large domains.

Performance surpasses classical grid sampling in efficiency and reliability.

Abstract

Ballistic capture orbits offer safer Mars injection at longer transfer time. However, the search for such an extremely rare event is a computationally intensive process. Indeed, it requires the propagation of a grid sampling the whole search space. This work proposes a novel ballistic capture search algorithm based on Taylor differential algebra propagation. This algorithm provides a continuous description of the search space compared to classical grid sampling research and focuses on areas where the nonlinearities are the largest. Macroscopic analyses have been carried out to obtain cartography of large sets of solutions. Two criteria, named consistency and quality, are defined to assess this new algorithm and to compare its performances with classical grid sampling of the search space around Mars. Results show that differential algebra mapping works on large search spaces, and automatic domain splitting captures the dynamical variations on the whole domain successfully. The consistency criterion shows that more than 87% of the search space is guaranteed as accurate, with the quality criterion kept over 80%.