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The chaos of double pendulums.

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The Math Flow

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32,280 Aufrufe • vor 14 Tagen •via X (Twitter)

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Yes, but only for a while. In this simulation, 20 nearly identical pendulums start together, then diverge after a few seconds, the time horizon of predictability. Chaos doesn’t mean randomness, just sensitivity.
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A double pendulum demonstrates chaos theory, tracing its unpredictable path The dependence on initial conditions, and sensitivity to variation is one of the fundamental properties of chaos This is commonly referred to as "the butterfly effect,"
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Chaos and the double pendulum: the configuration space of the double pendulum is a torus (a circle for each angle coordinate) so we can plot the evolution of such a pendulum in two ways: either as a "real pendulum" in physical space, or as a point in configuration space :)
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Chaos and the double pendulum: the configuration space of the double pendulum is a torus (a circle for each angle coordinate) so we can plot the evolution of such a pendulum in two ways: either as a "real pendulum" in physical space, or as a point in configuration space :)

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