Reduction of Truncation Error in Computing Symplectic State Transition Matrix

Abstract

This paper describes a high precision computation method of deriving general symplectic state transition matrices. Respecting the symplectic structure of state transition matrices is important in such a field as accurate, yet computationally efficient dynamic filters, longterm propagations of the motions of formation flying spacecraft and the eigenstructure/manifold analysis of N-body dynamics etc. The method proposed in this paper is a post-processing to improve or add a symplectic property to arbitrary state transition matrices. Since this method can be combined with any state transition matrix derivation schemes, it works as a truncation error reduction and also provides a simple way to add the symplectic property to matrices derived with non-symplectic methods. We present the derivation, its applicability and numerical evaluations when applied to a twobody dynamics, an Earth orbit with perturbation forces based on the real ephemeris and a circular restricted three-body problem.