Quick Start

Waterwheel Model

Model Type
SES Library XPP model

This model describes the dynamics of a waterwheel. The wheel has 10 cups that are filled when as they pass over the top of the arc of the wheel (imagine a Ferris wheel where instead of seats there are buckets. Water is flowing down on the Ferris wheel filling the buckets). The weight of the water makes the wheel turn. However, in this model, the buckets leak. So if the flow of the water from the top is too slow, some interesting motion can occur.

This waterwheel model is a perfect physical representation the Lorenz model. The water wheel exhibits a chaotic motion. That is, the direction and speed of spinning is unpredictable.

Reference

German Guillermo Theler (2004). Poster presentation titled, \"Lorenzian chaotic waterwheel\". Link: http://ib.cnea.gov.ar/~thelerg/pdf/wheel2004.pdf.

Default Dynamics
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Waterwheel
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Download Animation File (waterwheel.ani)

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$$\ddot{ heta}=\sum ^{N-1}_{i=0} \rho v_{i}gR \ \mbox {sin}\left ( heta+i \frac{2\pi}{N} \right )-k\dot{ heta}$$
$$\dot{ heta}=\ddot{ heta}$$
waterwheel_model.ode
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Download Source File (waterwheel_model.ode)

The source code file can be used with XPP/XPPAUT or other simulation tools.

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