Reducibility of Periodic Quasi-Periodic Systems

DOI: 10.4236/ijmnta.2014.31002   PDF   HTML   XML   3,565 Downloads   5,349 Views  

Abstract

In this work, the reducibility of quasi-periodic systems with strong parametric excitation is studied. We first applied a special case of Lyapunov-Perron (L-P) transformation for time periodic system known as the Lyapunov-Floquet (L-F) transformation to generate a dynamically equivalent system. Then, we used the quasi-periodicnear-identity transformation to reduce this dynamically equivalent system to a constant coefficient system by solving homological equations via harmonic balance. In this process, we obtained the reducibility/resonance conditions that needed to be satisfied to convert a quasi-periodic system in to a constant one. Assuming the reducibility is possible, we obtain the L-P transformation that can transform original quasi-periodic system into a system with constant coefficients. Two examples are presented that show the application of this approach.

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Ezekiel, E. and Redkar, S. (2014) Reducibility of Periodic Quasi-Periodic Systems. International Journal of Modern Nonlinear Theory and Application, 3, 6-14. doi: 10.4236/ijmnta.2014.31002.

Conflicts of Interest

The authors declare no conflicts of interest.

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