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

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URI: http://hdl.handle.net/10016/7159
ISSN: 0002-9505
DOI: https://www.doi.org/10.1119/1.17047
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deterministic_cuerno_ajp_1992_ps.pdf (1.92 MB)
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1992-01
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American Association of Physics Teachers
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Abstract
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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7 pages, 6 figures.-- PACS nrs.: 05.45.+b, 03.20.+i.
MR#: MR1145312 (92j:70028)
Keywords
Pendulums, Chaotic systems, Nonlinear problems, Elasticity, Poincaré mapping, Lyapunov method, Correlation functions, Power spectra
Bibliographic citation
American Journal of Physics, 1992, vol. 60, n. 1, p. 73-79
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