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Relative Equilibria of a Prolate Gyrostat with a Discrete Damper

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Abstract

We investigate the possible equilibria for a torque-free gyrostat with an attached springmass damper. The equations of motion are presented, and we develop explicit stability conditions for simple steady spins about principal axes using Routh-Hurwitz and Liapunov stability analyses. Numerical continuation determines additional equilibria using rotor momentum as the bifurcation parameter. Multiple equilibria are identified and characterized, including some interesting stable equilibria corresponding to steady spins about non-principal axes. Pitchfork bifurcations from the nominal-spin state are examined analytically using Liapunov-Schmidt reduction, which produces conditions on system parameters for avoiding a jump phenomenon.

The views expressed in this article are those of the authors and do not reflect the official policy or position of the United States Air Force, Department of Defense, or the US Government.

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Author notes

  1. Ralph A. Sandfry (Formerly Ph.D. Candidate)

    Present address: Currently, Director of Operations, Detachment 4, Air Force Operational Test and Evaluation Center, Peterson Air Force Base, Colorado, 80914, USA

Authors and Affiliations

  1. Aerospace and Ocean Engineering, Virginia Polytechnic Institute and State University, Blacksburg, Virginia, 24061, USA

    Ralph A. Sandfry (Formerly Ph.D. Candidate) & Christopher D. Hall (Associate Professor)

Authors
  1. Ralph A. Sandfry
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  2. Christopher D. Hall
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Sandfry, R.A., Hall, C.D. Relative Equilibria of a Prolate Gyrostat with a Discrete Damper. J of Astronaut Sci 50, 367–387 (2002). https://doi.org/10.1007/BF03546244

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