Dynamics of flexible spinning satellites with radial wire antennas
Abstract
A dynamic analysis is presented for a spin stabilized spacecraft employing four radial wire antennas with tip masses, a configuration first employed in the IMPJ spacecraft. The use of wires in place of the usual booms represents the ultimate in weight reduction at the expense of flexibility. The satellite is modelled as a 14 degree of freedom system, and the linearized equations of motion are found. The lowest order vibrational modes and natural frequencies of the gyroscopically coupled system are then determined. Because the satellite spin rate is decreased by antenna deployment, a spinup maneuver is needed. The response of the time varying mode equations during spinup is found, for the planar modes, in terms of Bessel functions and a Struve function of order 0.25. Because tables of the latter are not readily available, the particular solution is expressed in various forms including an infinite series of Bessel functions and a particularly useful asymptotic expansion. An error formula for the latter is derived showing that it gives good accuracy. Also, a simple approximation to the complementary function is obtained using the WKB method, and the phase error in the approximation is shown to be small.
 Publication:

Acta Astronautica
 Pub Date:
 February 1976
 DOI:
 10.1016/00945765(76)900916
 Bibcode:
 1976AcAau...3...17L
 Keywords:

 Flexible Bodies;
 Satellite Antennas;
 Spin Dynamics;
 Spin Stabilization;
 Equations Of Motion;
 Explorer 50 Satellite;
 Linear Equations;
 Resonant Frequencies;
 Vibration Mode;
 WentzelKramerBrillouin Method;
 Astrodynamics