Dynamics of flexible spinning satellites with radial wire antennas
Abstract
A dynamic analysis is presented for a spinstabilized spacecraft employing four radial wire antennas with tip masses. The satellite is modelled as a 14degreeoffreedom system, and the linearized equations of motion are found. The lowestorder 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 timevarying mode equations during spinup is found for the planar modes in terms of Bessel functions and a Struve function of order 0.25. 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. A simple approximation to the complementary function is obtained using the WenzelKramersBrillouin 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