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

Amit K. Sanyal, Jinglai Shen, N. Harris McClamroch, Anthony M. Bloch

Research output: Contribution to journalArticlepeer-review

33 Scopus citations


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 languageEnglish (US)
Pages (from-to)833-842
Number of pages10
JournalJournal of Guidance, Control, and Dynamics
Issue number5
StatePublished - 2005
Externally publishedYes

ASJC Scopus subject areas

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


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