APPROACHING NONLINEAR DYNAMICS BY STUDYING THE MOTION OF A PENDULUM I: OBSERVING TRAJECTORIES IN STATE SPACE

Author:

HENG H.1,DOERNER R.1,HÜBINGER B.1,MARTIENSSEN W.1

Affiliation:

1. Physikalisches Institut der Universität Frankfurt am Main, D-60054 Frankfurt am Main 1, Germany

Abstract

A phenomenological introduction to concepts of nonlinear dynamics is given. A driven pendulum is used as an appropriate model to demonstrate characteristic features of the dynamics of nonlinear systems. The mechanical and electronic setup of the pendulum is described and quantified in detail, and different techniques to visualize the motion in state space are discussed. Finally, a “road map” in parameter space is calculated which provides a tool for finding special scenarios by choosing appropriate driving amplitudes and frequencies.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modeling and Simulation,Engineering (miscellaneous)

Cited by 23 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Self-sustained vibrations in the system of a bi-harmonically driven pendulum;Physics Letters A;2022-03

2. Harmonic and Nonlinear Resonances;Springer Series in Synergetics;2015-12-01

3. Bibliography;Simulations of Oscillatory Systems;2015-02-05

4. Stability Boundaries of Transiently Non-autonomous Chaotic Nonlinear System: Graphical Approach;Chaos and Complex Systems;2012-12-19

5. CONTROL AND SYNCHRONIZATION OF CHAOTIC PENDULUM USING BACKSTEPPING;International Journal of Modern Physics B;2010-07-10

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