Deterministic chaos in the elastic pendulum: a simple laboratory for nonlinear dynamics
| dc.contributor.author | Fernández-Rañada, Antonio | |
| dc.date.accessioned | 2023-06-20T18:58:06Z | |
| dc.date.available | 2023-06-20T18:58:06Z | |
| dc.date.issued | 1992-01 | |
| dc.description | © 1992 American Association of Physics Teachers. Two of the authors (RC and JJR) acknowledge A. Muñoz and L.A. Fernández for their encouragement, and A. Sánchez for his help in typing this manuscript. | |
| dc.description.abstract | The chaotic motion of the elastic pendulum is studied by means of four indicators, the Poincare 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. | |
| dc.description.department | Depto. de Estructura de la Materia, Física Térmica y Electrónica | |
| dc.description.faculty | Fac. de Ciencias Físicas | |
| dc.description.refereed | TRUE | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/25212 | |
| dc.identifier.doi | 10.1119/1.17047 | |
| dc.identifier.issn | 0002-9505 | |
| dc.identifier.officialurl | http://dx.doi.org/10.1119/1.17047 | |
| dc.identifier.relatedurl | http://scitation.aip.org | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/59016 | |
| dc.issue.number | 1 | |
| dc.journal.title | American Journal of Physics | |
| dc.language.iso | spa | |
| dc.page.final | 79 | |
| dc.page.initial | 73 | |
| dc.publisher | American Association of Physics Teachers | |
| dc.rights.accessRights | open access | |
| dc.subject.cdu | 537 | |
| dc.subject.keyword | Numerical Experiments | |
| dc.subject.keyword | Entropy | |
| dc.subject.keyword | Mass. | |
| dc.subject.ucm | Electricidad | |
| dc.subject.ucm | Electrónica (Física) | |
| dc.subject.unesco | 2202.03 Electricidad | |
| dc.title | Deterministic chaos in the elastic pendulum: a simple laboratory for nonlinear dynamics | |
| dc.type | journal article | |
| dc.volume.number | 60 | |
| dcterms.references | 1.- H.N. Núñez-Yépes, A.L. Salas-Brito, C.A. Vargas, L. Vicente, Onset of chaos in an extensible pendulum, Phys. Lett. A 145, 101-105, 1990. 2.- M.G. Olsson, Why doies a mass on a spring sometimes misbehave?, Am.J. Phys. 44, 1211-1212, 1976. 3.- H.M. Lai, On the recurrence phenomenon of a resonant spring pendulum, Am. J. Phys. 52, 219-223, 1984. 4.- Y. Cohen, S. Katz, A. Peres, E. Santo, R. Yitzhaki, Stroboscopic views of regular and chaotic orbits, Am. J. Phys. 56, 1042, 1988. 5.- M.V. Berry, Regular and irregular motion, in AIP Conference Proceedings, no. 46, edited by S. Jorna (American Institute of Physics, New York, 1978), pp. 16-120. 6.- V.I. Arnold, Mathematical Methods of Classical Mechanics (Springer-Verlag, New York, 1978), Chap. 10. 7.- A.J. Lichtenberg, M.A. Lieberman, Regular and Stochastic Motion (Springer-Verlag, Heidelberg, 1983), pp. 42 ff. 8.- J.M. Thompson, H.B. Stewart, Nonlinear Dynbamics and Chaos (Wiley, New York, 1986). 9.- H. Goldstein, Classical Mechanics (Addison-Wesley, Reading, MA, 1959), 2nd ed., pp. 457 ff. 10.- S.E. Koonin, Cpomputational Physics (Benjamin Cummings, Menlo Park, CA, 1986), Chap. 4. 11.- G.H. Walker, J. Ford, Amplitude instability and ergodic behavior for conservative nonlinear oscillator systems, Phys. REv. A 188, 416-432, 1969. 12.- G. Benettin, J.M. Strelcym, Numercial experiments on the free motion of a point mass moving in a plane convex region; Stochastic transition and entropy, Phys. Rev. A 17, 773-784, 1978. 13.- G. Benettin, G.L. Galgani, J.M. Strelcyn, Kolmogorov entropy and numerical experiments, Phys.Rev. A 14, 2338-2345, 1976. 14.- A.F. Rañada, Phenomenology of chaotic motion, in Methods of Applications of Nonlinear Dynamics, edited by A.W. Saenz (World Scientific, Singapore, 1988), 99. 1-93. 15.- P. Bergè, Y. Pomeau, Ch. Vidal, Order in Chaos (Aerial, Santa Cruz, CA, 1990). | |
| dspace.entity.type | Publication |
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