Summary
A method is described for determining stability diagrams for coupled Mathieu-equations. The boundary curves are found by searching for those almost-periodic solutions of the differential equations for which the real part of the characteristic exponent changes from zero to a non-zero value. The method derives analytic expressions for the involved determinants and is able to find the transition curves even for parameters that cannot be considered small.
Übersicht
Es wird eine Methode zur Ermittlung der Stabilitätsdiagramme für gekoppelte Mathieu-Gleichungen beschrieben. Die Grenzkurven der Stabilitätsbereiche werden erhalten, indem man nach jenen fastperiodischen Lösungen der Differentialgleichungen sucht, für die der Realteil des charakteristischen Exponenten von Null zu einem nichtverschwindenden Wert wechselt. Analytische Ausdrücke für die auftretenden Determinanten werden hergeleitet. Die Methode kann auch bei Parametern angewendet werden, die nicht klein sind.
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Hansen, J. Stability diagrams for coupled Mathieu-equations. Ing. arch 55, 463–473 (1985). https://doi.org/10.1007/BF00537654
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DOI: https://doi.org/10.1007/BF00537654