## Abstract

A dumbbell-shaped rigid body can be used to represent certain large spacecraft or asteroids with bimodal mass distributions. Such a dumbbell body is modeled as two identical mass particles connected by a rigid, massless link. Equations of motion for the five degrees of freedom of the dumbbell body in a central gravitational field are obtained. The equations of motion characterize three orbit degrees of freedom, two attitude degrees of freedom, and the coupling between them. The system has a continuous symmetry due to a cyclic variable associated with the angle of right ascension of the dumbbell body. Reduction with respect to this symmetry gives a reduced system with four degrees of freedom. Relative equilibria, corresponding to circular orbits, are obtained from these reduced equations of motion; the stability of these relative equilibria is assessed. It is shown that unstable relative equilibria can be stabilized by suitable attitude feedback control of the dumbbell.

Original language | English (US) |
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Pages (from-to) | 833-842 |

Number of pages | 10 |

Journal | Journal of Guidance, Control, and Dynamics |

Volume | 28 |

Issue number | 5 |

DOIs | |

State | Published - 2005 |

Externally published | Yes |

## ASJC Scopus subject areas

- Control and Systems Engineering
- Aerospace Engineering
- Space and Planetary Science
- Electrical and Electronic Engineering
- Applied Mathematics