### Abstract

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 language | English (US) |
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Article number | AAS 05-186 |

Pages (from-to) | 1381-1398 |

Number of pages | 18 |

Journal | Advances in the Astronautical Sciences |

Volume | 120 |

Issue number | II |

State | Published - Oct 26 2005 |

Event | AAS/AIAA Space Flight Mechaics Meeting - Spaceflight Mechanics 2005 - Copper Mountain, CO, United States Duration: Jan 23 2005 → Jan 27 2005 |

### All Science Journal Classification (ASJC) codes

- Aerospace Engineering
- Space and Planetary Science

### Cite this

*Advances in the Astronautical Sciences*,

*120*(II), 1381-1398. [AAS 05-186].