Double pendulum: An experiment in chaos

Levien, Richard Ben; Tan, Sijian

doi:10.1119/1.17335

Cited by 79 publications

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“…As a general nature of a complex system, the evolution elapses a very long time, where synchronization among many agents with different frequencies of oscillators has been often observed, via nonlinear interactions [9]. Such phase transition is already known in the simplest system of coupled oscillators, i.e., a double pendulum, as the transition from regular to irregular movement [10]. Hereafter, we will refer to one of the itinerant patterns as a phase even though the original literature denotes it as a class.…”

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confidence: 99%

The Phase Transition during Post Annealing

Nakagawa¹

2016

JPSA

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Abstract:We have studied why PA (post-annealing) takes a long time to restore damaged crystallinity, which corresponds to repeat 10 10 times of lattice vibrations. Using a MD (molecular dynamics) simulation, we monitored the time-series of the LRO (long-range order) parameter as LRO pattern, in the case of a type IIa diamond, from the beginning of ion impact by a sub-keV N 2 beam implantation to a few nanoseconds, i.e., close to the feasible time limit for MD simulations. Due to the ion impact, the LRO parameter changed gradually from "LRO = 1" (crystal) to "LRO = 0" (amorphous), showing the so-called critical slowing-down phenomenon. However, since PA was started the LRO pattern was not unique. The LRO patterns were grouped into more than three types of phases and the transition between them was also found. From the viewpoint of statistical dynamics, such chaotic variations in the LRO pattern may present that the system is a GCM (globally coupled map) of a complex system in a closed system. A GCM composed of coupled oscillators develops slowly to exhibit several different phases or 'chaotic itinerancy' over time. Therefore, the long duration required for PA may be attributable to the nature of a complex system.

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The Phase Transition during Post Annealing

Nakagawa¹

2016

JPSA

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“…Building a chaotic waterwheel �Physics� Observing bifurcations in a buckling beam �Civil Engineering� 1 Coupled pendulums �Physics� 16,17 The Mercury Beating Heart �Chemistry� It may be interesting to note that most of these experiments were undertaken using the facilities of an introductory studio lab, supplemented with supplies from the local hardware stores. In only a few instances did we have to borrow from the upper-division labs for items like digitizing oscilloscopes and frequency meters.…”

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

Sungar

Sharpe

Moelter

et al. 2001

American Journal of Physics

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We describe the implementation of a new laboratory-based interdisciplinary undergraduate course on nonlinear dynamical systems. Geometrical methods and data visualization techniques are especially emphasized. A novel feature of the course is a required laboratory where the students analyze the behavior of a number of dynamical systems. Most of the laboratory experiments can be economically implemented using equipment available in many introductory physics microcomputer-based laboratories.

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“…The case of the horizontal vibrations of the suspension point of the pendulum in presence of gravity and the case of the motion of the pendulum in weightlessness conditions under vibrations are of particular importance because no results of experiments which are related with induced stability of the double pendulum in such conditions. Note here, the chaotic motion of the pendulum and the effect noise vibrations have not been studied in this work because they are out of the object of this research [Levein and Tan, 1993], This papers consists of two parts. In the first part, the theoretical model used to study the induced stability is discussed.…”

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confidence: 99%

Double Pendulum Induced Stability

Nikolai

Gabin

Jiménez

2015

Int. J. Appl. Mechanics

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In this work, a study of the relative equilibrium of a double pendulum whose point of suspension performs high frequency harmonic vibrations is presented. In order to determine the induced positions of equilibrium of the double pendulum at different gravity and vibration configurations, a set of experiments has been conducted. The theoretical analysis of the problem has been developed using Kapitsa's method and numerical method. The method of Kapitsa allows to analyze the potential energy of a system in general and to find the values of the parameters of the problem that correspond to the relative extreme of energy -positions of stable or unstable equilibrium. The results of numerical and theoretical analysis of Hamilton equations are in good agreement with the results of the experiments.

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Double pendulum: An experiment in chaos

Cited by 79 publications

References 0 publications

The Phase Transition during Post Annealing

The Phase Transition during Post Annealing

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

Double Pendulum Induced Stability

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