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Higher-Order Averaging for Periodically Forced, Weakly Nonlinear Systems

K. Yagasaki
T. Ichikawa
Journal / Anthology

International Journal for Bifurcation and Chaos
Year: 1999
Volume: 9
Issue: 3
Page range: 519-531

We consider periodically forced, weakly nonlinear systems and perform higher-order averaging analyses. Especially, we describe an algorithm for computing the higher-order averaging terms by the Lie transforms. The necessary computations can be implemented on a developed package of the computer algebra system, Mathematica. We also give three examples for two Duffing-type oscillators with the primary or ultra-subharmonic resonance and a two-degree-of-freedom system with internal and external resonances, to demonstrate out results.

*Mathematics > Calculus and Analysis > Dynamical Systems