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Catastrophe

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Phil Todd

@polymnia

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L is the natural length of the spring AD.  AC is length 4.

Set L to be 3.  How many stable positions are there?  (You can drag D to different start points on the line and see where it goes.)

Try dragging B to rotate the line.  How does it affect the stable positions?

Now change L to 6, but move B so the line is horizontal.  How many stable positions are there?

Now move B  so that the line slopes down from D to C.  Observe that D moves slowly towards C until the stable point disappears and it moves "catastrophically" to the other stable point.

This example is from Steven H Strogatz Nonlinear Dynamics and Chaos

Tags: catastrophe, dynamics
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