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Deterministic chaos in the elastic pendulum: A simple laboratory for nonlinear dynamics

By Rodolfo Cuerno, Antonio Fernández Rañada and Juan Jesús Ruiz-Lorenzo


7 pages, 6 figures.-- PACS nrs.: 05.45.+b, 03.20.+i.MR#: MR1145312 (92j:70028)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.Publicad

Topics: Pendulums, Chaotic systems, Nonlinear problems, Elasticity, Poincaré mapping, Lyapunov method, Correlation functions, Power spectra, Matemáticas
Publisher: 'American Association of Physics Teachers (AAPT)'
Year: 1992
DOI identifier: 10.1119/1.17047
OAI identifier:

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