Deterministic chaos in the elastic pendulum: A simple laboratory for nonlinear dynamics
作者:
R. Cuerno,
A. F. Rañada,
J. J. Ruiz‐Lorenzo,
期刊:
American Journal of Physics
(AIP Available online 1992)
卷期:
Volume 60,
issue 1
页码: 73-79
ISSN:0002-9505
年代: 1992
DOI:10.1119/1.17047
出版商: American Association of Physics Teachers
关键词: PENDULUMS;CHAOTIC SYSTEMS;NONLINEAR PROBLEMS;ELASTICITY;POINCARE MAPPING;LYAPUNOV METHOD;CORRELATION FUNCTIONS;POWER SPECTRA
数据来源: AIP
摘要:
The chaotic motion of the elastic pendulum is studied by means of four indicators, the Poincaré section, the maximum Lyapunov exponent, the correlation function, and the power spectrum. It is shown that for very low and very large energies the motion is regular while it is very irregular for intermediate energies. Analytical considerations and graphical representations concerning the applicability of KAM theorem are also presented. This system and the type of description used are very suitable to introduce undergraduate students to nonlinear dynamics.
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