The Inverted Pendulum The Inverted Pendulum Rev 2.0 If you jiggle a pivot of an upside-down pendulum, up and down fast enough, the pendulum...
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The Inverted Pendulum Description

If you jiggle a pivot of an upside-down pendulum, up and down fast enough, the pendulum remains upside-down The Inverted Pendulum application was designed to graphically model a difficult-to-believe phenomenon. If you jiggle the pivot of an upside-down pendulum up and down fast enough, the pendulum remains upside-down. Suggested trial values for the various parameters are included. The suggested number of time-steps is 5000. I've now added the option to view the Phase Space plot for the motion. This is more the sort of thing a mathematician would look at, because it indicates qualitative aspects of the behaviour more clearly. It shows better what angle and angular velocity combinations are common, and which are "no-go" areas, for example. It may be impossible to spot a regular pattern from the actual motion - a Limit Cycle for instance. There is no Limit Cycle for the Inverted Pendulum, but the parameters are confined to defined values for the entire duration of the motion.

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