A laboratory-based nonlinear dynamics course for science and engineering students

Sungar, N.; Sharpe, John P.; Moelter, Matthew J.; Fleishon, Neil; Morrison, Kent E.; McDill, Jean Marie; Schoonover, Rod

doi:10.1119/1.1351147

Cited by 10 publications

(5 citation statements)

References 14 publications

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“…It is hoped that some of these results could be incorporated into standard mechanics courses that touch on the linear and nonlinear motions of a string, as well as theoretical and ex-perimental courses that are specifically focused on the study nonlinear dynamics. [12][13][14][15][16][17] For a basic background on some of the concepts and terms used in nonlinear dynamics and this paper-such as Hopf bifurcation, Logistic map, or Lorenz attractor, and so on-see an introductory text such as the book by Strogatz. 13…”

Section: Introductionmentioning

confidence: 99%

An experimental investigation into the dynamics of a string

Molteno

Tufillaro

2004

American Journal of Physics

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Section: Introductionmentioning

confidence: 99%

An experimental investigation into the dynamics of a string

Molteno

Tufillaro

2004

American Journal of Physics

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“…Currently, many works deal with nonlinear dynamics, studying and applying methods to better understand computational simulations [10][11][12][13]. Considering that most of the systems found in nature are nonlinear and that we can still see several chaotic features in parts of them, their study is critical, and their teaching should be started as soon as possible on undergraduate courses [14][15][16][17]. However, the study of such systems takes great effort, due to the mathematical concepts and proofs involved in this [18].…”

Section: Introductionmentioning

confidence: 99%

Graphical interface as a teaching aid for nonlinear dynamical systems

et al. 2018

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Chaos theory is an important breakthrough in understanding nonlinear dynamical systems. It is generally accepted that chaotic systems involve transitivity, a high density of periodic points in metric space, and extreme sensitivity to changes in initial conditions. Many systems taught on undergraduate courses satisfy these conditions, such as electronic circuits or computer simulations of nonlinear dynamical systems. However, a good understanding of these concepts is broadly difficult to achieve on such courses, and especially so at the undergraduate level. In view of this, we have developed an interactive standalone graphical user interface, which is platform-independent. The interface didactically simulates six chaotic systems. It allows the user to study a particular system without prior knowledge of computer programming, demonstrating rich dynamical behaviour such as fixed points, periodic cycles and deterministic chaos. At the same time, the interface provides details of the simulation and the parameters used, as well as some of the leading references. We provide the complete code and a detailed installation guide, which should make it easy to use the interface reliably and with little overhead work. We also provide a comparison with other available software for reference, and as a guide to readers who would like to explore this fascinating subject in more depth or with alternative approaches. Lastly, we present the results of a survey

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“…On the other hand, Mancuso [17,18] shows empirically-but only in a qualitative way-the existence of a bifurcation, using a manually controlled experimental device (the Groove Tube). The system is also experimentally investigated in the context of a nonlinear dynamics course using traditional (analog) video techniques, obtaining quantitatively the bifurcation diagram [19]. However, in all these references the authors remain within the limits of the point-particle approximation-even in cases when the actual 'bead' is a sphere that rolls over the interior surface of the hoop-and the experimental side of the question is not explored exhaustively.…”

Section: Introductionmentioning

confidence: 99%

“…The (colour) bands represent the theoretical model uncertainty due to the experimental error in the parameters R 0 and α. The discontinuous vertical lines indicate the resonant frequency for the point particle model (red line, equation (12)) and the rigid sphere model (green line, equation(19)) respectively. The distance between these lines is more than the absolute error of the angular velocity.…”

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confidence: 99%

The bead on a rotating hoop revisited: an unexpected resonance

et al. 2016

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The bead on a rotating hoop is a typical problem in mechanics, frequently posed to junior science and engineering students in basic physics courses. Although this system has a rich dynamics, it is usually not analysed beyond the point particle approximation in undergraduate textbooks, nor empirically investigated. Advanced textbooks show the existence of bifurcations owing to the system's nonlinear nature, and some papers demonstrate, from a theoretical standpoint, its points of contact with phase transition phenomena. However, scarce experimental research has been conducted to better understand its behaviour. We show in this paper that a minor modification to the problem leads to appealing consequences that can be studied both theoretically and empirically with the basic conceptual tools and experimental skills available to junior students. In particular, we go beyond the point particle approximation by treating the bead as a rigid spherical body, and explore the effect of a slightly non-vertical hoop's rotation axis that gives rise to a resonant behaviour not considered in previous works. This study can be accomplished by means of digital video and open source software. The experience can motivate an engaging laboratory project by integrating standard curriculum topics, data analysis and experimental exploration.

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A laboratory-based nonlinear dynamics course for science and engineering students

Cited by 10 publications

References 14 publications

An experimental investigation into the dynamics of a string

An experimental investigation into the dynamics of a string

Graphical interface as a teaching aid for nonlinear dynamical systems

The bead on a rotating hoop revisited: an unexpected resonance

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