Doppelpendel

This program calculates the motion of a double pendulum that exhibits deterministic chaos at large deflections. It is possible to calculate two such pendulums in parallel with slightly different initial conditions in order to demonstrate that the movement is completely different after a short time. If you switch to linearizing the differential equation, chaos no longer occurs.

Enter the initial conditions for the two angles and angular velocities of the pendulum arms in degrees or rad/sec and then click on "Start". To calculate two identical pendulums with slightly different initial conditions, check the box for "Second double pendulum". The second pendulum is displayed in green, but may initially be covered by the red pendulum. The difference in the initial conditions is entered via a deviation of the outer arm compared to the first (red) pendulum in the "Deviation" box. By ticking the "Linearize" box, a corresponding but linear differential equation is solved using the approximations sin(x)=x and cos(x)=1.

The coupled non-linear differential equations are solved using the 4th order Runge-Kutta method with a step size of 0.5ms. The pendulum arms have a length of l=1m and the acceleration due to gravity is g=9.^81m/s2. The representation is not in real time but results from the calculation speed. The differential equations to be solved are as follows: