Sensitivity Analysis of Separation Time Along Weak Stability Boundary Transfers

Author:

Isabel Nolton, Kento Tomita, Yuri Shimane, Koki Ho

Keyword:

Nonlinear Sciences, Chaotic Dynamics, Chaotic Dynamics (nlin.CD), Optimization and Control (math.OC)

journal:

date:

2024-02-01 00:00:00

Abstract

This study analyzes the sensitivity of the dynamics around Weak Stability Boundary Transfers (WSBT) in the elliptical restricted three-body problem. With WSBTs increasing popularity for cislunar transfers, understanding its inherently chaotic dynamics becomes pivotal for guiding and navigating cooperative spacecrafts as well as detecting non-cooperative objects. We introduce the notion of separation time to gauge the deviation of a point near a nominal WSBT from the trajectory's vicinity. Employing the Cauchy-Green tensor to identify stretching directions in position and velocity, the separation time, along with the Finite-Time Lyapunov Exponent are studied within a ball of state uncertainty scaled to typical orbit determination performances.

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