In the space of the system parameters, the stability charts are determined for the delayed and damped Mathieu equation defined as This stability chart makes the connection between the Strutt-Ince chart of the damped Mathieu equation and the Hsu-Bhatt-Vyshnegradskii chart of the autonomous second order delay-differential equation. The combined charts describe the intriguing stability properties of an important class of delayed oscillatory systems subjected to parametric excitation.
Stability of the Damped Mathieu Equation With Time Delay
Contributed by the Dynamic Systems and Control Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received by the ASME Dynamic Systems and Control Division, May 2002; final revision, December 2002. Associate Editor: N. Olgac.
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Insperger, T., and Ste´pa´n, G. (June 4, 2003). "Stability of the Damped Mathieu Equation With Time Delay ." ASME. J. Dyn. Sys., Meas., Control. June 2003; 125(2): 166–171. https://doi.org/10.1115/1.1567314
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