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Keywords: Mathieu equation
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Proceedings Papers

A Simple Approach for the Computation of Lyapunov-Floquet Transformations for the Mathieu Equation

Ashu Sharma
Proc. ASME. IDETC-CIE2021, Volume 9: 17th International Conference on Multibody Systems, Nonlinear Dynamics, and Control (MSNDC), V009T09A048, August 17–19, 2021
Publisher: American Society of Mechanical Engineers
Paper No: DETC2021-71028
https://doi.org/10.1115/DETC2021-71028
.... Mathieu equation is investigated in this work and L-F transformations and their inverse are generated for stable and unstable cases. These transformations are very useful in the design of controllers using time-invariant methods and in the bifurcation studies of nonlinear time-periodic systems. time...
View Paper titled, A Simple Approach for the Computation of Lyapunov-Floquet Transformations for the <span class="search-highlight">Mathieu</span> <span class="search-highlight">Equation</span>
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Topics: Bifurcation, Computation, Control equipment, Design, Differential equations, Eigenvalues, Theorems (Mathematics)
Proceedings Papers

Stabilization of Inverted Coupled Pendula Using Parametric Excitation

Reiko Osada, Chikara Sato
Proc. ASME. DETC97, Volume 1C: 16th Biennial Conference on Mechanical Vibration and Noise, V01CT12A001, September 14–17, 1997
Publisher: American Society of Mechanical Engineers
Paper No: DETC97/VIB-4008
https://doi.org/10.1115/DETC97/VIB-4008
... Abstract Parametric stabilization of a single inverted pendulum has been extensively studied using the Mathieu equation and its corresponding stability diagram. The inverted single pendulum may be stabilized using parametric excitation at a specified frequency and amplitude given by a narrow...
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Topics: Excitation, Pendulums
Proceedings Papers

Optimal Feedback Controls of Linear Systems With Time Delay

Jie Sheng, Ozer Elbeyli, J. Q. Sun
Proc. ASME. IDETC-CIE2003, Volume 5: 19th Biennial Conference on Mechanical Vibration and Noise, Parts A, B, and C, 2015-2035, September 2–6, 2003
Publisher: American Society of Mechanical Engineers
Paper No: DETC2003/VIB-48547
https://doi.org/10.1115/DETC2003/VIB-48547
... or open. Semi-discretization delayed feedback control optimal feedback gains root locus time-delayed linear systems Mathieu equation Optimal Feedback Controls of Linear Systems with Time Delay Jie Sheng, Ozer Elbeyli and J. Q. Sun Department of Mechanical Engineering Proceedings of DETC’03...
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Topics: Delays, Feedback, Linear systems