- 00-408 Michele V. Bartuccelli, Guido Gentile, Kyriakos V. Georgiou
- On the dynamics of a vertically driven damped planar pendulum
Oct 18, 00
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Abstract. The dynamics of the planar pendulum with parametric vertical
time-periodic forcing is considered.
Analytical and numerical methods are employed to study
the various dynamical features of the system.
A rigorous analysis is presented in order to show that,
in presence of friction, the upward equilibrium position
becomes asymptotically stable when the period of the forcing
is below an appropriate threshold;
this is illustrated by performing numerical computations
and advanced visualization techniques.
Also the dynamics of the system far from its equilibrium points
is systematically investigated by using Poincare'
sections and phase portraits.
The attractors and the associated basins of attraction
are computed. Furthermore we calculate the Lyapunov
exponents to show that for some parameter values the dynamics
of the pendulum shows sensitivity to initial conditions.