Asymmetric Body Spinning Motion with Energy Dissipation and Constant Body-Fixed Torques

Abstract

The spinning motion of an asymmetric body under the ine uence of both energy dissipation and constant body- e xed torques is investigated using a generic semirigid model with a spherical slug surrounded by a viscous layer. Thestudy objectivewastoachieveamorefundamentalunderstandingofthegeneralspinningmotionofasemirigid spacecraftduringatypicalspin-upmaneuver,ae at-spintransitionmaneuver,and/orae at-spinrecoverymaneuver. Asetofnondimensionalequationsofmotion isderivedforthestability analysisofequilibrium points. Inparticular, three-dimensional phase-space trajectories are studied for three different cases of constant body-e xed torques along the major, intermediate, or minor axis. For these cases with energy dissipation, some new analytical as well as computer simulation results are discussed in terms of equilibrium manifolds, separatrix surfaces, periodic or nonperiodic solutions, etc. OR a torque-free semirigid body with internal energy dissi- pation, the kinetic energy decreases and the energy ellipsoid becomes smaller with time. This results in an open polhode path that spirals outward from the minor axis, crosses the separatrix, and approaches the major axis. Consequently, a spacecraft spinning about its minor axis in the presence of energy dissipation is said to be unstable; i.e., the spacecraft will eventually reorient and spin about its major axis with either a positive or negative spin rate. A classic example oftheminor-axisinstabilityphenomenonis thee rst U.S. satellite, Explorer I, launched in 1958. Although a spacecraft spinning about its minor axis is unstable in the presence of internal energy dissipation, spacecraft are often required to spin about their minor axis for several reasons. Fairing constraints of most launch vehicles require that the minor axis of the payload spacecraft be aligned with the longitudinal axis of the launch vehicles. Furthermore, most launch vehicles spin about their longitudinal axis before payload separation, resulting in a minor- axis spin of the spacecraft after separation. Somelaunchvehiclesorupperstagesdonothavespin-upcapabil- ity for payload spacecraft and spin-up of the spacecraft is achieved after separation.Because ofinitial angular rates atseparation,a typ- ical spin-up maneuver usually results in a residual nutation angle andaspin-axisprecessionfromtheseparationattitude.Thespinrate selection depends on many factors, including the pointing accuracy requirement. Spacecraft spinning about their minor axis are often stabilized using an active nutation control system consisting of thrusters and accelerometers. Spinning spacecraft are also required to spin down or reorient their spin axis during the various phases of spacecraft operation. Forexample, aspin-axisreorientation isrequired to align the spacecraft spin axis in the proper direction for apogee-kick mo- tor e ring. After apogee-kick motor burn, a spin-axis reorientation is also required to orient the spin axis to the orbit normal. During the operational life of spin-stabilized spacecraft, periodic spin-axis re- orientationmaneuversarealsorequiredtocompensatefortheeffects ofexternaldisturbance torques,primarily causedby solarpressures. One of the simplest rotational maneuvers is the reorientation of the spin axis of a spacecraft using internal energy dissipation. A