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Chaos and the double pendulum
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Small changes in start give very different motion.
A double pendulum is deterministic but chaotic: tiny differences in start grow exponentially, so long-term prediction is impossible.
Release two nearly identical double pendulums to see them diverge.
Chaotic doesn't mean random.
In more detail
A double pendulum, two pendulums attached end to end, shows chaotic motion. Small changes in initial conditions produce very different outcomes over time, even though the equations are deterministic.
Real-world uses
- Double pendulums are used to teach chaos theory.
- Chaos ideas apply to weather forecasting and planetary dynamics.
- A double pendulum shows how sensitive a chaotic system is: a tiny change in starting angle produces a very different path.
Open the interactive lesson, with simulation and quiz →
Frequently asked questions
Is the double pendulum random?
No, it is deterministic, but its sensitivity makes long-term prediction impossible in practice.
Why is it important?
It shows that simple systems can behave chaotically.
Does chaos mean the motion is random?
No. It is fully determined by its equations, but tiny differences in the start grow so fast that long-term prediction is impossible.
Related topics in Oscillations & SHM
Lissajous figures · Anharmonic oscillation · Nonlinear oscillators · Parametric resonance · Oscillation of a floating body · Liquid in a U-tube