Imagine a double pendulum consisting of two pieces with different constant lengths and constant masses. This double pendulum dissipates no energy.
- When you let it go, you can vary the two angles in the pendulum and the angular momenta of the pieces or the potential energy of the DP. When will the strange attractor pattern ("ordered" chaos) arise for the DP?
- If so, how does it look like (in 3d)?
Other examples of a strange attractor are the Rössler attractor, which can be associated with the chaotic behavior of a dripping tap or a fibrillating heart, or the Lorenz attractor with its now quite iconic butterfly shape. They all follow for certain values in a set of non-linear coupled differential equations, which in the Lorenz attractor are the rate of convection (in 2d) on the x-axis and the temperature on the y- and z-axis The form of the attractor can be seen in this 3d space.
The coupled pendulum has four coupled differential equations (corresponding to the two angles and two angular momenta), but I couldn't find how the strange attractor looks like (which is impossible for four variables) in 3d.