Why is a double pendulum so chaotic?

A double pendulum executes simple harmonic motion (two normal modes) when displacements from equilibrium are small. 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.

Why is it called a chaotic pendulum?

For one of the pendulums the starting angle for the lower mass is just 0.01 degrees different than the other pendulum—so they essentially start with the same initial conditions. When any system is highly dependent on the initial conditions it is considered a chaotic system.

What is the purpose of double pendulum?

The double pendulum is widely used in education, research, and applications. For example, the double pendulum is a staple benchtop experiment for introducing and studying chaos and state transitions. It has also been used to study chaos both experimentally [1], [2], [3] and numerically [4], [5].

What causes chaotic motion?

Chaotic behavior exists in many natural systems, including fluid flow, heartbeat irregularities, weather and climate. It also occurs spontaneously in some systems with artificial components, such as the stock market and road traffic.

Is a pendulum chaotic?

The chaotic behavior of pendulum is usually associated with the random force acting on a pendulum (Brownian motion). Another type of chaotic motion (deterministic chaos) occurs in nonlinear systems with only few degrees of freedom.

Is a pendulum a chaotic system?

A damped driven pendulum is a chaotic system. In a chaotic system the future behavior is highly dependent on the exact value of the initial conditions. A tiny change in initial conditions can cause huge changes after a short period of time.

What is chaotic motion?

Ref: wikipedia. So chaotic motions may be defined as those random motions which works dynamically on such objects where the present trajectory of motion of object can’t determine the future approximated trajectory.

How do you determine if a system is chaotic?

The usual test of whether a deterministic dynamical system is chaotic or nonchaotic is the calculation of the largest Lyapunov exponent λ. A positive largest Lyapunov exponent indicates chaos: if λ > 0, then nearby trajectories separate exponentially and if λ < 0, then nearby trajectories stay close to each other.

How does electromagnetic pendulum work?

As the pendulum’s magnet accelerates towards the electromagnet’s core, the Hall effect sensor registers an increase in voltage. The voltage peaks as the pendulum passes overhead, and as soon as the Hall Effect sensor detects the drop in voltage, the electromagnet flicks on for a moment to propel the pendulum away.

What is a chaotic pendulum?

Chaotic Pendulum. Coupled, double, physical pendulum executes chaotic motion when non-linear initial conditions are imposed. A double pendulum executes simple harmonic motion (two normal modes) when displacements from equilibrium are small.

What type of motion does a double pendulum execute?

A double pendulum executes simple harmonic motion (two normal modes) when displacements from equilibrium are small. 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.

What is a planar double pendulum?

Referring to Figure 1, the planar double pendulum we consider consists of two pendula that swing freely in the vertical plane and are connected to each other by a smooth pin joint, where each pendulum comprises a light rigid rod with a concentrated mass on one end.

What are the dimensions of the pendulum?

The two arms of the upper pendulum are fabricated from 1/4″ thick aluminum and the lower pendulum from 1/2″ thick aluminum. The pendulum lengths are approximately 10.75″ and their masses are equal. The general design was adapted from an MIT version provided to us by Jack Wisdom.