Canonical Modelling of Relative Spacecraft Motion Via Epicyclic Orbital Elements

Authors: Kasdin, N.¹; Gurfil, Pini²; Kolemen, Egemen³

Source: Celestial Mechanics and Dynamical Astronomy, Volume 92, Number 4, August 2005 , pp. 337-370(34)

Publisher: Springer

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Abstract:

This paper presents a Hamiltonian approach to modelling spacecraft motion relative to a circular reference orbit based on a derivation of canonical coordinates for the relative state-space dynamics. The Hamiltonian formulation facilitates the modelling of high-order terms and orbital perturbations within the context of the Clohessy–Wiltshire solution. First, the Hamiltonian is partitioned into a linear term and a high-order term. The Hamilton–Jacobi equations are solved for the linear part by separation, and new constants for the relative motions are obtained, called epicyclic elements. The influence of higher order terms and perturbations, such as Earth’s oblateness, are incorporated into the analysis by a variation of parameters procedure. As an example, closed-form solutions for J₂-invariant orbits are obtained.

Keywords: Hamiltonian dynamics; relative motion; perturbations; formation flying

Document Type: Research article

DOI: http://dx.doi.org/10.1007/s10569-004-6441-7

Affiliations: 1: Mechanical and Aerospace Engineering Department, Princeton University, Princeton, NJ, 08544, USA, Email: jkasdin@princeton.edu 2: Faculty of Aerospace Engineering, Technion – Israel Institute of Technology, Haifa, 32000, Israel, Email: pgurfil@technion.ac.il 3: Mechanical and Aerospace Engineering Department, Princeton University, Princeton, NJ, 08544, USA, Email: ekolemen@princeton.edu

Publication date: 2005-08-01