EAN: 9783031796449

SYNTHESIS LECTURES ON MECHANICAL ENGINEERING ...

The inherent complex dynamics of a parametrically excited pendulum is of great interest in
nonlinear dynamics  which can help one better understand the complex world. Even though the
parametrically excited pendulum is one of the simplest nonlinear systems  until now  complex
motions in such a parametric pendulum cannot be achieved. In this book  the bifurcation
dynamics of periodic motions to chaos in a damped  parametrically excited pendulum is
discussed. Complete bifurcation trees of periodic motions to chaos in the parametrically
excited pendulum include: period-1 motion (static equilibriums) to chaos  and period- motions
to chaos ( = 1  2  ···  6  8  ···  12). The aforesaid bifurcation trees of periodic motions to
chaos coexist in the same parameter ranges  which are very difficult to determine through
traditional analysis. Harmonic frequency-amplitude characteristics of such bifurcation trees
are also presented to show motion complexity and nonlinearity in such a parametrically excited
pendulum system. The non-travelable and travelable periodic motions on the bifurcation trees
are discovered. Through the bifurcation trees of travelable and non-travelable periodic motions
the travelable and non-travelable chaos in the parametrically excited pendulum can be achieved.
Based on the traditional analysis  one cannot achieve the adequate solutions presented herein
for periodic motions to chaos in the parametrically excited pendulum. The results in this book
may cause one rethinking how to determine motion complexity in nonlinear dynamical systems.

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