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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



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