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[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 >