Bounded, periodic relative motion using canonical epicyclic orbital elements

N. Jeremy Kasdin, Egemen Kolemen

Research output: Contribution to journalConference articlepeer-review

11 Scopus citations


In this paper, we use a Hamiltonian approach to derive the equations of motion for an object relative to a circular or slightly elliptical reference orbit. By solving the Hamilton-Jacobi equation we develop constants of the relative motion called epicyclic elements. A perturbation Hamiltonian is formulated in order to derive variational equations for the " constants" via Hamilton's equations. We use this formalism to derive bounded, periodic orbits in the presence of various perturbations. In particular, we show a simple no-drift condition that guarantees bounded orbits in the presence of J 2 forces. We also derive the relative motion deviations and boundedness conditions due to eccentricity of the reference orbit and higher-order terms in the gravitational potential.

Original languageEnglish (US)
Article numberAAS 05-186
Pages (from-to)1381-1398
Number of pages18
JournalAdvances in the Astronautical Sciences
Issue numberII
StatePublished - 2005
EventAAS/AIAA Space Flight Mechaics Meeting - Spaceflight Mechanics 2005 - Copper Mountain, CO, United States
Duration: Jan 23 2005Jan 27 2005

All Science Journal Classification (ASJC) codes

  • Aerospace Engineering
  • Space and Planetary Science


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