Double Pendulum as a chaotic system

Maritime News Marine Weather
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The official discover of modern chaos theory was a meteorologist, Edward Lorenz. Lorenz was playing with computer models to simulate weather.

A double pendulum executes simple harmonic motion (two normal modes) when displacements from equilibrium are small. However, when large displacements are imposed, the non-linear system becomes dramatically chaotic in its motion and demonstrates that deterministic systems are not necessarily predictable.

A double pendulum executes simple harmonic motion (two normal modes) when displacements from equilibrium are small. However, when large displacements are imposed, the non-linear system becomes dramatically chaotic in its motion and demonstrates that deterministic systems are not necessarily predictable.

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The startling divergence was rooted in the subtle discrepancy of the printout values, rounded to a mere three decimal places, lacking the accuracy incorporated in the original calculations. Lorenz had anticipated that any deviations resulting from this loss in precision would be minor, however, they spiraled out of control. The errors escalated rapidly, doubling approximately every four days of simulated weather, and within the span of two simulated months, the weather scenario bore no resemblance to the initial conditions.

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