Series Expansion Form of an Approximate State Transition Matrix for Fully Perturbed Orbits

概要

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This paper presents an approximation method of the state transition matrix for orbits around a primary body and subject to arbitrary perturbation forces. By assuming that the behavior of the perturbation sources is sufficiently slow compared with the orbital period, which covers most of practically useful cases for orbits around a primary attracting body, this method provides a functional form of the approximate state transition matrix composed of a sum of elementary analytic functions. The resulting state transition matrix is expressed in a series expansion form with a small number of constant parameter matrices and osculating orbit parameters at the initial epoch, and is valid for several tens of orbital revolutions without updating the parameters. Numerical simulations show that this method is valid for arbitrary eccentricity orbits with the semimajor axis ranging from LEO up to around 10 Earth radii when applied to Earth orbits. Due to the simplicity of the resulting approximate form, the formulation provided in this paper is suited for implementation onboard spacecraft, and a fast and iterative computation of linearized orbital dynamics with full perturbation forces.