Poincare section for double pendulum

*To*: mathgroup at smc.vnet.net*Subject*: [mg120573] Poincare section for double pendulum*From*: gal bevc <gal.bevc at gmail.com>*Date*: Fri, 29 Jul 2011 08:02:28 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com

Hello, I'm a relatively new user of Mathematica, who doesn't have much of programming skills. For my undergraduate assingment I must analyze chaotic motion of double pendulum. Until now i have got system of differential equations for equations of motion for double pendulum(i have x''[t]=function(t) and y''[t]=function(t)). System of differential equations can be solved for 4 inital conditions, x[0],y[0],x'[0] and y'[0]. With using function NDSolve i got functions of angles and angular velocities for upper and lower pendulum with respect to time, x[t],x'[t],y[t] and y'[t]. To get a poincare section of double pendulum, i have to record position of y[t] and y'[t] whenever x[t] is equal to zero and the velocity of x'[t] is a positive number. In the end I must get some sort of phase diagram y[t] and y'[t]. Because this is a Hamilton non-dissipative system, inital energy of the system is a constant of time and initial energy is a function of initial conditions. To get a real poincare diagram i must repeat the procedure described above for different initial conditions, but for the same energy level. I need mathematica to use some random numbers for initial conditions in a way that the initial energy of the system stays the same. So i must repeat procedure for poincare section(surface of section) for let's say 50 different initial conditions and then display all results in one y[t],y'[t] diagram. Hope that someone can help me. Thank you, Gal Bevc