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Double Pendulum Chaotic Gymnastics

Bar-and-ring double pendulum oscillates in a surprising way that defies intuition. The pendulum is a damped mechanical oscillator whose energy dissipates continuously after it is set in motion. When displacements from equilibrium are small, the pendulum executes simple harmonic motion (normal mode). However, when large displacements are imposed, the non-linear system becomes dramatically chaotic in its motion and demonstrates that deterministic systems are not necessarily predictable. Chapters: 00:13 Steady State, Quasi-Harmonic Oscillations – Small Torque Applied 00:22 Chaotic motion – Torque Applied by Force of Gravity 00:52 Fleeting Moment of Hesitation 01:06 Steady State – Quasi-Harmonic Oscillations 01:18 Chaotic motion – Torque Applied by Force of Gravity 02:08 Steady State – Quasi-Harmonic Oscillations Forces that affect the pendulum include the manual torque applied to activate the pendulum, gravitational force, and centrifugal force. The word "chaos" is confusing, if one interprets it in the nontechnical sense of common language - "lack of order". In fact, deterministic chaotic systems such as this pendulum, are quite ordered and theoretically predictable. If we knew the initial state of a chaotic system in perfect detail, measured all parameters of the surrounding medium continuously, applied these data to a mathematical model on a computer, we would still be constrained the speed of calculations. Even if we deployed a quantum computer that could solve non-linear differential equations exactly, the computation would still lag behind the changing parameters by some infinitesimal unit of time. One of the first scientists to comment on chaos was Henri Poincaré, a late-nineteenth-century French mathematician who extensively studied topology and dynamic systems. Poincaré explained, “It may happen that a small difference in the initial conditions produce very great ones in the final phenomena. A small error in the former will produce an enormous error in the latter. Prediction becomes impossible.” Dr. Nicolas Rott, of the Swiss Federal Institute of Technology in Zurich, was the first to utilize chaotic pendulums. He carried out research and analysis on pendulums as a means of demonstrating the principles of chaos and in 1970 published his findings in a document titled “A Multiple Pendulum for the Demonstration of Non-Linear Coupling.” Check out a collection of double pendulums that display chaotic motion:    • Double Pendulum Chaotic Motion   Music: Take Five Composer: Paul Desmond Artists: Dave Brubeck Quartet Dave Brubeck – piano Paul Desmond – alto saxophone Gene Wright – upright bass Joe Morello – drums Label: Columbia Released: 1959 #CoupledOscillators #beatmode #EnergyTransfer #doublependulum