Canonical modelling of relative spacecraft motion via epicyclic orbital elements

N. Jeremy Kasdin, Pini Gurfil, Egemen Kolemen

Research output: Contribution to journalArticlepeer-review

47 Scopus citations


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 J 2-invariant orbits are obtained.

Original languageEnglish (US)
Pages (from-to)337-370
Number of pages34
JournalCelestial Mechanics and Dynamical Astronomy
Issue number4
StatePublished - Aug 2005

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation
  • Mathematical Physics
  • Astronomy and Astrophysics
  • Space and Planetary Science
  • Computational Mathematics
  • Applied Mathematics


  • Formation flying
  • Hamiltonian dynamics
  • Perturbations
  • Relative motion


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