Chaotic motion under parametric excitation

The chaotic behaviour of a parametrically excited system is studied in some detail. An example of such a system is seen in the transverse vibration of a buckled column under axial excitation. The existence of homoclinic orbits for the parametrically excited system is predicted by Melnikov's method. Lyapunov exponents, Poincare maps, power spectra and other characteristics of chaotic motions are analysed numerically to confirm the results. An experiment on a buckled column is also carried out to qualitatively verify the theoretical results.

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