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Mathieu Equation (Parametric Oscillator)

by Siva Srinivas Kolukula

 

29 Dec 2011

Numerical and phase plane analysis of Mathieu equation / parametric oscillator

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Description

When the pivot of simple pendulum is excited periodically in vertical direction, it gives Mathieu equation. Numerical and phase plane analysis of Mathieu equation is done using ODE45. Stability, instability of the parametric oscillator is discussed. Stability chart for the MAthieu equation is given. Parametric resonance behavior is shown and discussed.
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Acknowledgements
This submission has inspired the following:
Stability Chart
Required Products MATLAB
MATLAB release MATLAB 7.10 (2010a)
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mathieu equation Siva Srinivas Kolukula 29 Dec 2011 08:29:12
parametric oscillator Siva Srinivas Kolukula 29 Dec 2011 08:29:12
ode45 Siva Srinivas Kolukula 29 Dec 2011 08:29:12
phase plane Siva Srinivas Kolukula 29 Dec 2011 08:29:12
rungekutta method Siva Srinivas Kolukula 29 Dec 2011 08:29:12
stability Siva Srinivas Kolukula 29 Dec 2011 08:29:12
instability Siva Srinivas Kolukula 29 Dec 2011 08:29:12
parametric instability Siva Srinivas Kolukula 29 Dec 2011 08:29:12
parametric resonance Siva Srinivas Kolukula 29 Dec 2011 08:29:12
simple pendulum Siva Srinivas Kolukula 29 Dec 2011 08:29:12
driven pendulum Siva Srinivas Kolukula 29 Dec 2011 08:29:12
nonlinear resonance Siva Srinivas Kolukula 29 Dec 2011 08:29:12
subharmonic resonance Siva Srinivas Kolukula 29 Dec 2011 08:29:12

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