×

zbMATH — the first resource for mathematics

Deterministic chaos in the elastic pendulum: a simple laboratory for nonlinear dynamics. (English) Zbl 1219.70060
Summary: 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 the KAM theorem are also presented. This system and the type of description used are very suitable to introduce undergraduate students to nonlinear dynamics.

MSC:
70K50 Bifurcations and instability for nonlinear problems in mechanics
34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
70H05 Hamilton’s equations
PDF BibTeX XML Cite
Full Text: DOI