Improved Directional State Transition Tensors for Accurate Aerocapture Performance Analysis
For mission designers and guidance/navigation engineers, this provides a practical semi-analytical propagation method for aerocapture, which is a challenging regime dominated by nonconservative forces.
This work develops novel dynamics analysis techniques to identify effective reduced-dimension bases for directional state transition tensors (DSTTs), enabling accurate and computationally efficient aerocapture performance analysis. The proposed DSTTs significantly reduce computational cost while maintaining accuracy in predicted apoapsis radius and terminal energy, outperforming traditional DSTTs for key state subsets.
Aerocapture is particularly challenging for semi-analytical propagation because the dynamics are dominated by nonconservative forces whose magnitudes vary significantly throughout 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, computing higher-order STTs requires integrating exponentially many equations as the state dimension increases. 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 predicted apoapsis radius and terminal energy. 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.