TITLE:
Reducibility of Periodic Quasi-Periodic Systems
AUTHORS:
Evi Ezekiel, Sangram Redkar
KEYWORDS:
L-P Transformation; Quasi-Periodic System; Reducibility
JOURNAL NAME:
International Journal of Modern Nonlinear Theory and Application,
Vol.3 No.1,
March
17,
2014
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.