# Labs

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.

hline

## Contents

- 1 Completely inelastic bouncing ball
- 2 Metronome or biological synchronization
- 3 Dynamics of a hopping robot
- 4 Mechanical time delay oscillator
- 5 Fluid flow oscillations
- 6 Stick-slip dynamics of dry friction
- 7 Fracture fractals
- 8 Chemical oscillator
- 9 Stabilizing a unicycle
- 10 Plastic bottle oscillator
- 11 Spinning hoop or bead on a hoop bifurcations
- 12 Damped driven pendulum
- 13 Chaotic circuits
- 14 Lorenz waterwheel
- 15 Faraday waves
- 16 Vertically vibrated inverted pendulum
- 17 Double pendulum

## Completely inelastic bouncing ball

## Metronome or biological 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.

## 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