       Re: Poincare section for double pendulum

• To: mathgroup at smc.vnet.net
• Subject: [mg120589] Re: Poincare section for double pendulum
• From: "Christoph Lhotka" <christoph.lhotka at univie.ac.at>
• Date: Sat, 30 Jul 2011 06:00:47 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com

```Hello,

this is just a starting point...

Try to solve your problem with the method "EventLocator" in NDSolve to
limit your output to values on the PoincarÃ© surface of section.
You could use e.g. FindInstance to get a good set of initial conditions
for given energy value of the Hamiltonian.

Good luck,

Christoph

On 29/07/2011 14:02, gal bevc wrote:
> 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,y,x' and y'. 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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