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Topic: Poincare section for double pendulum
Replies: 4   Last Post: Aug 3, 2011 6:23 AM

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Christoph Lhotka

Posts: 41
Registered: 3/2/10
Re: Poincare section for double pendulum
Posted: Jul 30, 2011 5:26 AM
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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 Poincaré 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,


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[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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