Rott's Chaotic Pendulum

Описание: Rott’s damped double pendulum exhibits two modes of motion: regular, linear, and predictable, the other is chaotic, nonlinear, and unpredictable.

When the frequency of the entire pendulum system is one half of the red pendulum, the two pendulums draw energy from each other at a slow periodic rate. The exchange of energy period contains many pendulum-oscillation periods and this motion reproduces itself with great accuracy.

When one pendulum oscillates with maximum amplitude, the other stands almost still and the process reverses itself as the energy passes from one pendulum to the other. This process, which is associated with low energy and small amplitudes, is linear, including the coupling effect.

At very large amplitude oscillations, especially when the pendulums have enough energy to overturn (high-energy initial conditions), the behavior becomes chaotic. Chaotic or unpredictable behavior is usually associated with sensitivity to the initial data. Chaotic behavior implies that two slightly different initial conditions give rise to solution that differ greatly, one of the defining features of chaotic dynamical systems.

Chapters
00:15 Anatomy of Rott’s Pendulum
00:35 Rott’s Pendulum – Regular Motion
01:23 Rott’s Pendulum – Chaotic Motion, clockwise
02:30 Last gasp: red pendulum overturns 11 consecutive times
03:57 Rott’s Pendulum – Chaotic Motion, counterclockwise

View various coupled pendulums in action:
   • Coupled Pendulums  

Explore a series of chaotic Pendulums:
   • Chaotic Pendulums Series  

Music
Title: Down The Street Blues
Artist: Unicorn Heads
Album: River Radio, Released 2018

#CoupledOscillators #beatmode #EnergyTransfer #doublependulum