Canonical Modelling of Relative Spacecraft Motion Via Epicyclic Orbital Elements |
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Authors: | Email author" target="_blank">N?Jeremy?KasdinEmail author Pini?Gurfil Egemen?Kolemen |
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Institution: | (1) Mechanical and Aerospace Engineering Department, Princeton University, Princeton, NJ 08544, USA;(2) Faculty of Aerospace Engineering, Technion – Israel Institute of Technology, Haifa, 32000, Israel |
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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. |
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Keywords: | Hamiltonian dynamics relative motion perturbations formation flying |
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