Double pendulum - LMSE Christchurch Centre
A mechatronically measurable double pendulum that can produce nonlinear time series data.
The double pendulum is an example of dynamical system that exhibits chaotic dynamics. Whilst there have been many papers describing the theoretical aspects of chaos, there have been few that examine these theories rigorously on a physical device. It is the purpose of this report to outline the development of a physical double pendulum system from which discrete measurements of the enclosures of the angular positions of the arms can be made. We describe the electronic system that transfers the measurement data to a host PC and the host software to store the measurements for further analysis using enclosure methods. Our device is a prerequisite for rigourous parameter estimation in machine interval experiments using techniques from computer-aided proofs in analysis.
Details are provided to facilitate easy replication of this mechatronically measurable double pendulum.
Making Sense out of Chaos (MathsReach.org)
"A Mechatronically Measurable Double Pendulum for Machine Interval Experiments", Piers Lawrence, Michael Stuart, Richard Brown, Warwick Tucker and Raazesh Sainudiin -- Indian Statistical Institute Technical Report, isibang/ms/2010/11, October 25, 2010 (PDF 900KB)
Time series of the angular position of each arm for two trajectories that were initialized similarly
Download the data of trajectory 1 and trajectory 2
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Last modified on Friday, 02-Sep-2016 12:54:23 MST and served on Thursday, 30-Mar-2023 16:21:53 MST.