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Relative Equilibria of a Rigid Satellite in a Circular Keplerian Orbit

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Abstract

We examine relative equilibria of a rigid body free to rotate about its center of mass which is constrained to follow a Keplerian orbit in a central gravitational field. We derive a noncanonical Hamiltonian formulation of this system and show how it relates to the noncanonical system for an unconstrained rigid body in a hierarchy of approximations of the two-body problem. For a particular approximation of the potential, the Keplerian system is equivalent to the classical approximation typically seen in the literature. We determine relative equilibria for this approximation and derive stability conditions for both arbitrary and axisymmetric bodies.

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Authors and Affiliations

  1. Department of Aeronautics and Astronautics, Air Force Institute of Technology, Wright-Patterson Air Force Base, OH, 45433, USA

    Jeffrey A. Beck (Doctoral Candidate, Member AAS)

  2. Space Vehicles Directorate, Air Force Research Laboratory, Kirtland AFB, NM, 87117, USA

    Jeffrey A. Beck (Doctoral Candidate, Member AAS)

  3. Department of Aeronautics and Astronautics, Air Force Institute of Technology, Wright-Patterson Air Force Base, OH, 45433, USA

    Christopher D. Hall (Assistant Professor, Senior Member AAS)

  4. Department of Aerospace and Ocean Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA, 24061, USA

    Christopher D. Hall (Assistant Professor, Senior Member AAS)

Authors
  1. Jeffrey A. Beck
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  2. Christopher D. Hall
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Beck, J.A., Hall, C.D. Relative Equilibria of a Rigid Satellite in a Circular Keplerian Orbit. J of Astronaut Sci 46, 215–247 (1998). https://doi.org/10.1007/BF03546235

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  • DOI: https://doi.org/10.1007/BF03546235

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