Where is the seperatrix on a double pendulum?

[dave1234]

Hi I am trying to investigate chaos and a double pendulum. Howvere I am stuck for whcih direction to go in. I want to find the point at which the double pendulum shows chaotic behavior. Having read a few peioces here and there, i have an idea that if i could determine when the pendulum crosses a seperatrix then this might be th point I am looking for. But where is the seperatrix on a dpouble pendulum? Also I am gogin to do this experiment as a practical and am wondering what measurment si can take in order to get some results, of a numerical order, and to plot some graphs, or maybe some phase portraits to show the chaotic behavior.

Any other help on double pendulum investigatons would be helpful.

thanx

 

[Valerie Park]

The separatrix is typically defined as the region in phase space (the set of all possible positions and velocities of a system) that separates trajectories with distinct behaviors. In a double pendulum, the separatrix is a curve in the 3-dimensional phase space which separates trajectories that will eventually return to the same position from those that will not. To determine when the pendulum crosses the separatrix, you can measure the position of the pendulum at regular intervals over time, and calculate its velocity and acceleration. When these three values cross certain thresholds, it indicates that the pendulum has crossed the separatrix.In order to plot a phase portrait, you will need to measure the position of the pendulum at regular intervals over time, as well as its velocity and acceleration. You can then use these three values to plot points on the phase portrait, which will show the behavior of the system over time. Finally, to investigate chaos, you will need to look for signs of deterministic chaos, such as sensitive dependence on initial conditions, fractal patterns in the phase portrait, and the presence of strange attractors.