Improved Directional State Transition Tensors for Accurate Aerocapture Performance Analysis

TL;DR

This paper introduces improved directional state transition tensors (DSTTs) tailored for aerocapture analysis, significantly reducing computational cost while maintaining accuracy in key orbital parameters, thus enhancing guidance and navigation strategies.

Contribution

The work develops novel basis selection techniques for DSTTs, enabling efficient and accurate aerocapture performance prediction with reduced computational effort.

Findings

DSTTs constructed along effective bases reduce computational cost.

DSTTs maintain accuracy in apoapsis and energy predictions.

Certain DSTTs outperform traditional methods in nonlinear perturbation propagation.

Abstract

Aerocapture is a unique challenge for semi-analytical propagation because its nonconservative dynamics lead to force magnitudes that vary substantially across the trajectory. State transition tensors (STTs), higher-order Taylor series expansions of the solution flow, have been widely used as a computationally efficient semi-analytical propagation method for orbital scenarios, but have not previously been applied to aerocapture. However, obtaining the higher-order STTs requires integrating exponentially more equations. Directional state transition tensors (DSTTs) mitigate this cost by projecting the state into a reduced-dimension basis. This work develops novel dynamics analysis techniques to identify effective bases for this reduction, including augmented higher-order Cauchy Green tensors tailored to quantities of interest such as apoapsis radius. Results show that DSTTs constructed along these bases significantly reduce computational cost while maintaining accuracy in apoapsis and energy prediction. In particular, certain of these DSTTs outperform traditional DSTTs in nonlinear perturbation propagation for key state subsets and quantities of interest. These results establish STTs and DSTTs as practical tools for aerocapture performance analysis to enable robust guidance and navigation.