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. 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 spin-up maneuver is needed. The response of the time-varying mode equations during spin-up 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 Wenzel-Kramers-Brillouin method, and the phase error in the approximation is shown to be small.
- Publication:
-
Acta Astronautica
- Pub Date:
- February 1976
- DOI:
- 10.1016/0094-5765(76)90091-6
- 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;
- Wentzel-Kramer-Brillouin Method;
- Astrodynamics