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

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

Research output: Contribution to journalArticle

28 Citations (Scopus)

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 languageEnglish (US)
Pages (from-to)833-842
Number of pages10
JournalJournal of Guidance, Control, and Dynamics
Volume28
Issue number5
DOIs
StatePublished - Jan 1 2005
Externally publishedYes

Fingerprint

Relative Equilibria
Equations of motion
Gravity
Gravitation
stabilization
Stabilization
degrees of freedom
Degree of freedom
gravity
gravitation
Equations of Motion
equations of motion
Orbits
symmetry
Asteroids
Right ascension
Orbit
Attitude control
Symmetry
Feedback control

ASJC Scopus subject areas

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

Cite this

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

In: Journal of Guidance, Control, and Dynamics, Vol. 28, No. 5, 01.01.2005, p. 833-842.

Research output: Contribution to journalArticle

Sanyal, Amit ; Shen, Jinglai ; McClamroch, N. Harris ; Bloch, Anthony M. / Stability and stabilization of relative equilibria of dumbbell bodies in central gravity. In: Journal of Guidance, Control, and Dynamics. 2005 ; Vol. 28, No. 5. pp. 833-842.
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