Summary
The linear stability of the attitude of a tethered satellite system, consisting of an asymmetric satellite with two equal tethered masses arranged vertically, is studied. The differential equations of motion are established, the attitude stability conditions are found, and then entered into a Magnus triangle. It is concluded that a tether parameterΔ has a significant effect on the satellite's attitude stability. By increasing the value of Δ, the stable regions in the Magnus triangle grow, until they cover more than half of its area, and then decline to exactly one half.
Übersicht
Die lineare Stabilität der Orientierung, d. h. der Winkellage, eines Systems aus einem starren Hauptsatelliten mit zwei im Schwerefeld vertikal an Seilen befestigten Punktmassen wird untersucht. Die Bewegungsgleichungen werden hergeleitet, deren Stabilitätsgrenzen berechnet und ins Magnussche Formdreieck eingetragen. Es wird gezeigt, daß der Seilparameter Δ einen entscheidenden Einfluß auf das Stabilitätsverhalten hat. Je größer der Seilparameter ist, desto grïoßer werden die Stabilitätsgebiete, bis sie mehr als die Hälfte des Magnusschen Formdreiecks ausmachen, um bei weiterem Ansteigen dann auf genau die Hälfte zurückgehen.
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Rimrott, F.P.J., Pan, R. Attitude stability of a tethered satellite in locked rotation. Ing. arch 60, 419–430 (1990). https://doi.org/10.1007/BF00531253
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DOI: https://doi.org/10.1007/BF00531253