Complicated Regular and Chaotic Motions of the Parametrically Excited Pendulum
نویسنده
چکیده
Several new types of regular and chaotic behavior of the parametrically driven pendulum are discovered with the help of computer simulations. A simple physical explanation is suggested to the phenomenon of subharmonic resonances. The boundaries of these resonances in the parameter space and the spectral composition of corresponding stationary oscillations are determined theoretically and verified experimentally. A close relationship between the upper limit of stability of the dynamically stabilized inverted pendulum and parametric resonance of the non-inverted pendulum is established. Most of the newly discovered modes are still waiting a plausible physical explanation.
منابع مشابه
Regular and Chaotic Motions of the Parametrically Forced Pendulum: Theory and Simulations
New types of regular and chaotic behaviour of the parametrically driven pendulum are discovered with the help of computer simulations. A simple qualitative physical explanation is suggested to the phenomenon of subharmonic resonances. An approximate quantitative theory based on the suggested approach is developed. The spectral composition of the subharmonic resonances is investigated quantitati...
متن کاملSynchronization of chaos in non-identical parametrically excited systems
In this paper, we investigate the synchronization of chaotic systems consisting of non-identical parametrically excited oscillators. The active control technique is employed to design control functions based on Lyapunov stability theory and Routh–Hurwitz criteria so as to achieve global chaos synchronization between a parametrically excited gyroscope and each of the parametrically excited pendu...
متن کاملSeismic Rehabilitation of Liquid Storage Tanks using Friction Pendulum Base Isolation subjected to the Near-Fault Ground Motions
Cylindrical liquid storage tanks are considered as vital structures in industrial complex whose nonlinear dynamic behavior is of crucial importance. Some of these structures around the world have demonstrated poor seismic behavior over the last decades. There are several methods and techniques for rehabilitation and reducing damages in these structures which among them passive control devices, ...
متن کاملMany pulses heteroclinic orbits with a Melnikov method and chaotic dynamics of a parametrically and externally excited thin plateMinghui
The multi-pulse heteroclinic orbits with a Melnikov method and chaotic dynamics in a parametrically and externally excited thin plate are studied in this paper for the first time. The thin plate is subjected to transversal and in-plane excitations, simultaneously. The formulas of the thin plate are derived from the von Kármán equation and Galerkin’s method. The method of multiple scales is used...
متن کاملAutoparametric Vibrations of a Nonlinear System with Pendulum
Vibrations of a nonlinear oscillator with an attached pendulum, excited by movement of its point of suspension, have been analysed in the paper. The derived differential equations of motion show that the system is strongly nonlinear and the motions of both subsystems, the pendulum and the oscillator, are strongly coupled by inertial terms, leading to the so-called autoparametric vibrations. It ...
متن کامل