The Damped Mathieu Equation
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We establish an asymptotic lower bound for the minimum excitation needed to cause instability for the damped Mathieu equation. The methods used are Floquet theory and Lyapunov-Schmidt, and we use a fact about the width of the instability interval for the undamped Mathieu equation. Our results are compared with published numerical data.
(1993). The Damped Mathieu Equation. Quarterly of Applied Mathematics, 51 (2), 389-398.