Astronomy and Astrophysics – Astronomy
Scientific paper
Aug 2005
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2005cemda..92..337k&link_type=abstract
Celestial Mechanics and Dynamical Astronomy, Volume 92, Issue 4, pp.337-370
Astronomy and Astrophysics
Astronomy
6
Hamiltonian Dynamics, Relative Motion, Perturbations, Formation Flying
Scientific paper
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.
Gurfil Pini
Kasdin Jeremy N.
Kolemen Egemen
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