The Simple Pendulum is Not Chaotic


Below is a demonstration that the simple pendulum is insensitive to initial conditions.

The two pendula (left and right) are identical, apart from their initial conditions (initial conditions are the way in which a system is started). The initial conditions for the simple pendulum are the starting angle, and the initial speed. The starting angles are the same in each case, but the initial speeds are as shown.

Left: Init. speed = 50 degrees/sec Right: Init. speed = 55 degrees/sec

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Key to graphs below: Left system - red line; right system - blue line


The two trajectories are so close that they are indistinguishable!

The two pendula stay in phase. This shows that the systems are not sensitive to their initial conditions. Such simple pendula are not chaotic.

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