### 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) |
---|---|

Pages (from-to) | 833-842 |

Number of pages | 10 |

Journal | Journal of Guidance, Control, and Dynamics |

Volume | 28 |

Issue number | 5 |

DOIs | |

State | Published - Jan 1 2005 |

Externally published | Yes |

### Fingerprint

### ASJC Scopus subject areas

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

### Cite this

*Journal of Guidance, Control, and Dynamics*,

*28*(5), 833-842. https://doi.org/10.2514/1.10546

**Stability and stabilization of relative equilibria of dumbbell bodies in central gravity.** / Sanyal, Amit; Shen, Jinglai; McClamroch, N. Harris; Bloch, Anthony M.

Research output: Contribution to journal › Article

*Journal of Guidance, Control, and Dynamics*, vol. 28, no. 5, pp. 833-842. https://doi.org/10.2514/1.10546

}

TY - JOUR

T1 - Stability and stabilization of relative equilibria of dumbbell bodies in central gravity

AU - Sanyal, Amit

AU - Shen, Jinglai

AU - McClamroch, N. Harris

AU - Bloch, Anthony M.

PY - 2005/1/1

Y1 - 2005/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=26244457794&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=26244457794&partnerID=8YFLogxK

U2 - 10.2514/1.10546

DO - 10.2514/1.10546

M3 - Article

AN - SCOPUS:26244457794

VL - 28

SP - 833

EP - 842

JO - Journal of Guidance, Control, and Dynamics

JF - Journal of Guidance, Control, and Dynamics

SN - 0731-5090

IS - 5

ER -