Chaotic image---The wandering of double pendulum

A colleague saw my double pendulum program a few days ago and asked me, "What is this crap?", I gave him a look of the eye said: "No culture, no education." So high-cornered things, you actually said hanging the son of a bum!

The previous article is about the "three-body" of the chaotic image, this article on a somewhat similar to the "double pendulum." Double pendulum is a concept in physics, vaguely remember that middle school physics talked about the pendulum. First, the definition of the pendulum and the double pendulum is given:

A simple pendulum: a device that is not elongated, does not have a mass, is fixed at the top, and a particle at the lower end.

Double pendulum: A composite object formed by the fulcrum of a pendulum mounted in the lower part of another pendulum. The double pendulum has two pendulum angles, so there are two degrees of freedom. Double pendulum is one of the simplest mechanical models of vibration system with multiple degrees of freedom, and it is also an example of chaos.

So the question is: Is this chaotic system of double pendulum, if given initial conditions, can be calculated at any later time of the motion state?

The answer is: theoretically possible, but in the actual calculation, due to the error, the results of the operation and the actual difference between the more and more large. This is similar to the three-body, which is so capricious in nonlinear mathematics.

This uses the script code of my definition syntax to generate a chaotic image. Related software see: Ychaos generating chaotic images. If you are interested in a graphic image of students, welcome to join QQ Group: 367752815. The image is generated by using the motion trajectory of the second pendulum point to generate the image.

First, the script code:

[Scriptlines]s=[Static]PW=[Static]qa=l*l* (m+N) b=l*n*h*cos (S-W) C=l* (N*h*sin (s-w) *v*v + (m+n) *g*sin (s)) d=n*h*l*cos (S-W) e=n*h*HF=n*h* (-l*sin (s-w) *u*u + g*sin (w)) I= (c*e-b*f)/(b*d-a*e) J= (a*f-c*d)/(b*d-a*e) U=u+i*TV=v+j*TS=s+u*TW=w+v*TX=l*sin (s) + h*sin (w) y=-l*cos (s)-h*cos (w) [Variables]g=9.800000h=2.000000L=1.000000m=1.000000N=2.000000P=1.000000Q=2.000000T=0.000500u=0.000000v=0.000000

Here is the use of angle changes to achieve double pendulum, the reference information is:

Http://sebug.net/paper/books/scipydoc/double_pendulum.html

Look at the Image:

Related software:

Ychaos Generating Chaotic images

Related articles:

Program realization of Double pendulum

Chaotic image---The wandering of double pendulum