Abstract
Harmonic analysis of the normal modes in the spin plane of a satellite with four hinged wire booms each with a tip mass attached is presented. Analytical expressions of normal mode coordinates and frequencies are obtained by solving the matrix eigenvalue equations, using secular determinant and simultaneous diagonalization methods. Translational oscillation of the center body is present in configurations of lower symmetry. The analytical results are in good agreement with computer simulations.
Zusammenfassung
Für einen Satelliten mit vier Drahtentenen, die mit Endgewichten versehen sind, wird die harmonische Analyse der Normalschwingungen ausgeführt. Analytische Ausdrücke für die Normalkoordinaten und-frequenzen werden abgeleitet, in denen die Eigenwert-Matrizengleichungen gelöst werden unter Benutzung der charakteristischen Polynome und simultaner Diagonalisierung. Translative Schwingung des Zentralkörpers existiert für Konfigurationen niedrigerer Symmetrie. Die analytischen Ergebnisse zeigen gute Übereinstimmung mit Komputersimulationen.
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References
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Lai, S.T., Mahon, H. & Smiddy, M. Dynamics of wire boom oscillations on a spinning satellite Part II, normal modes in spin plane. Journal of Applied Mathematics and Physics (ZAMP) 30, 12–29 (1979). https://doi.org/10.1007/BF01597477
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DOI: https://doi.org/10.1007/BF01597477