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MathGroup Archive 2009

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Differential Equation, pendulum, change of variable plot

  • To: mathgroup at smc.vnet.net
  • Subject: [mg99213] Differential Equation, pendulum, change of variable plot
  • From: gareth <schmit at hotmail.co.uk>
  • Date: Thu, 30 Apr 2009 06:21:01 -0400 (EDT)

Hello, thanks for taking the time to help sort out my query.

I am in the middle of investigating non linear pendulum. 
The equations of motion are 
w'[t]=-(1/q)w[t]-Sin[θ[t]] + g Cos[wD t]

Theta is the displacement, w the frequency, wD the driving frequency and g the drive amplitude.
Basically so far a I have plotted w vs theta to show chaos, however now I want to create a bifurcation diagram,
like this http://www.physics.drexel.edu/~gbyrne/Bif_g.jpg
This is done as far as I know is plotting w at the start of every drive cycle against g.
But I cant figure out how to do this,
maybe so sort of Do loop with the NDSolve of the differential equation.
Any help would be much appreciated


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