Labs

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Below is a list of possible nonlinear dynamics experiments. For the student led experiments groups should choose one from below of supply an alternative experiment with a short proposal arguing for its applicability.

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Completely inelastic bouncing ball

Group project from 2011

Metronome or biological synchronization

Metronome synchronization

Dynamics of a hopping robot

http://arxiv.org/abs/1208.6289

Mechanical time delay oscillator

http://ajp.aapt.org/resource/1/ajpias/v62/i3/p227_s1

Fluid flow oscillations

http://ajp.aapt.org/resource/1/ajpias/v75/i10/p893_s1?isAuthorized=no

Stick-slip dynamics of dry friction

http://pre.aps.org/abstract/PRE/v49/i6/p4973_1

http://www.nature.com/nature/journal/v367/n6463/abs/367544a0.html

Fracture fractals

http://pre.aps.org/abstract/PRE/v67/i6/e066209

http://prl.aps.org/abstract/PRL/v67/i4/p457_1

Chemical oscillator

The B-Z reaction is described here

Stabilizing a unicycle

http://ajp.aapt.org/resource/1/ajpias/v66/i7/p589_s1?isAuthorized=no

Plastic bottle oscillator

http://ajp.aapt.org/resource/1/ajpias/v75/i10/p893_s1?isAuthorized=no

Spinning hoop or bead on a hoop bifurcations

http://ajp.aapt.org/resource/1/ajpias/v71/i10/p999_s1?isAuthorized=no

Damped driven pendulum

http://ajp.aapt.org/resource/1/ajpias/v73/i12/p1122_s1?isAuthorized=no

Chaotic circuits

From Wikipedia, the free encyclopedia Chua's circuit is a simple electronic circuit that exhibits classic chaos theory behavior. It was introduced in 1983 by Leon O. Chua, who was a visitor at Waseda University in Japan at that time. The ease of construction of the circuit has made it a ubiquitous real-world example of a chaotic system, leading some to declare it a paradigm for chaos.

http://ajp.aapt.org/resource/1/ajpias/v72/i4/p503_s1?isAuthorized=no

Lorenz waterwheel

The Lorenz waterwheel is a physical device which is modeled by the Lorenz equations. The equations take the name of Ed Lorenz the scientist who discovered them while studying weather dynamics.

YouTube video of water wheel

Faraday waves

Faraday waves are the observed phenomena when a fluid with a free surface is vibrated sinusoidally above critical shaking parameters. Faraday waves are a classic example of a pattern forming system and display many features associated with nonlinear dynamics such as bifurcations and chaos.

Vertically vibrated inverted pendulum

A pendulum can be stabilized in the "upside down" position by vertically oscillating the pendulum base. In this lab we will explore the transition to inverted stability.

Double pendulum

Wikipedia article here