Hamiltonian modelling of relative motion

N. Jeremy Kasdin, Pini Gurfil

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


This paper presents a Hamiltonian approach to modelling relative spacecraft motion based on derivation of canonical coordinates for the relative state-space dynamics. The Hamiltonian formulation facilitates the modelling of high-order terms and orbital perturbations while allowing us to obtain closed-form solutions to the relative motion problem. 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, they are called epicyclic elements. The influence of higher order terms and perturbations, such as the oblateness of the Earth, are incorporated into the analysis by a variation of parameters procedure. Closed-form solutions for J2- and J4-invariant orbits and for periodic high-order unperturbed relative motion, in terms of the relative motion elements only, are obtained.

Original languageEnglish (US)
Pages (from-to)138-157
Number of pages20
JournalAnnals of the New York Academy of Sciences
StatePublished - 2004

All Science Journal Classification (ASJC) codes

  • General Biochemistry, Genetics and Molecular Biology
  • General Neuroscience
  • History and Philosophy of Science


  • Hamiltonian modelling
  • Relative motion


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