Double Pendulum Chaos Light Writing (computer simulation) 4

[atatassault]

The rotation point for the second pendulum seems to be moving very fast at times. Would it ever tend towards infinity? And if so, how would that affect a real system?

[khyar]

@atatassault In order to reach infinite speed it would require infinite energy. In this system there is no input or output of energy, rather energy is conserved in an exchange between potential and kinetic energy. The maximum attainable speed at any time is ultimately limited by the initial energy of the system, which in this case is entirely in the form of gravitational potential energy. At the lowest point all this PE is converted to KE and vice-versa.

[atatassault]

@khyar Oh, yeah, I see now. Its entirely a free response, so it wouldn't ever go to infinity. I was mistakenly thinking from a user input scenario of say a robot arm being told to move in such a way that would require a joint velocity (or joint movement, if trying to cross a singularity) to go to infinity.

[CoreyView]

is this model in a frictionless environment or could this be simulated in the real world?

[TUNDRA2529]

@CoreyView frictionless. It returns to the original height at one point. With any damping(friction) it would not have enough energy

[khyar]

@CoreyView Yeah, frictionless. I wanted to show how even a very simple system with just two degrees of freedom, no forcing and no damping, is capable of exhibiting chaos. If there is any friction it would come in the form of numerical dissipation, which is the loss of energy through truncation of the numbers due to the finite precision of a digital computer (in this case 64-bit double).

[x89codered89x]

What numerical method did you use to solve this?

[khyar]

@x89codered89x Hi, I used the standard Runge-Kutta 4th order integration scheme.

[Chulpasa]

wow, this is amazing! keep up the good work

[khyar]

@Chulpasa Thank you, I will :-)

[stickervvigger]

Beautiful! thanks for the posts

[khyar]

@stickervvigger Thanks for your comment!