Minimal energy configurations of gravitationally interacting rigid bodies

Richard Moeckel

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


Consider a collection of n rigid, massive bodies interacting according to their mutual gravitational attraction. A relative equilibrium motion is one where the entire configuration rotates rigidly and uniformly about a fixed axis in R3. Such a motion is possible only for special positions and orientations of the bodies. A minimal energy motion is one which has the minimum possible energy in its fixed angular momentum level. While every minimal energy motion is a relative equilibrium motion, the main result here is that a relative equilibrium motion of n≥ 3 disjoint rigid bodies is never an energy minimizer. This generalizes a known result about point masses to the case of rigid bodies.

Original languageEnglish (US)
Pages (from-to)3-18
Number of pages16
JournalCelestial Mechanics and Dynamical Astronomy
Issue number1
StatePublished - May 1 2017

Bibliographical note

Funding Information:
Research supported by NSF Grant DMS-1208908.

Publisher Copyright:
© 2016, Springer Science+Business Media Dordrecht.


  • Celestial mechanics
  • Configurations
  • Rigid bodies


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