Directional State Transition Tensors for Capturing Dominant Nonlinear Effects in Orbital Dynamics

Abstract

Higher-order methods such as state transition tensors (STTs) have shown promise for a variety of applications in astrodynamics, but can be limited in their use due to their potentially large computational and storage requirements. In this paper we present a method for approximating STTs by aligning the STTs with particularly unstable directions. This strategy allows us to isolate the most important terms in the higher-order STTs and ignore any less important terms. This method, which we call directional state transition tensors (DSTTs), is applied to several examples in two- and three-body dynamic systems, and it is shown to perform well for both nonlinear state and state uncertainty propagation. The method produces similar results to the full STTs, but requires significantly fewer elements to be stored, which can result in up to improvements in speed for nonlinear uncertainty propagation computations. DSTTs are promising for expanding the use of STTs to situations with highly nonlinear dynamics but limited computational resources, such as on-board a spacecraft.