Nutational Stability and Core Energy of a Quasirigid Gyrostat
Abstract
The asymptotic nutational stability of a quasirigid gyrostat is analyzed. The primary purpose of this analysis is to resolve a debate concerning the use of the energy-sink method of analysis for systems containing driven rotors. It is shown that when the work done by the motor torque is not taken into account, the analysis leads to a contradiction even when the total energy is dissipative. A proper application of Landon's original idea yields a relationship between the time rate of change of Hubert's "core energy" and the energy dissipation rate of the damping mechanisms in the spacecraft. The analysis shows that the core energy might increase during a rotor
despin condition; hence, the minimality of core energyテ__a previous criterionテ__is not always guaranteed. A criterion for the design of the damper to insure dissipation of the core energy is presented; this condition is always satisfied for the case of a constant relative rotor spin speed that facilitates a "closed-form" solution to the
nutation angle time history of an axisymmetric gyrostat. The stability condition resulting from this analysis is
consistent with the Landon-Iorillo stability criterion.
Description
Journal of Guidance, Control and Dynamics
The article of record as published may be located at http://arc.aiaa.org/loi/jgcd
Rights
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.Related items
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