Re: Differential Equation, pendulum, change of variable plot

• To: mathgroup at smc.vnet.net
• Subject: [mg99304] Re: Differential Equation, pendulum, change of variable plot
• From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
• Date: Sat, 2 May 2009 05:59:41 -0400 (EDT)
• References: <gtbtrf\$249\$1@smc.vnet.net>

```Hi,

it should be a differential equation second order for a
pendulum and if it is non-autonomous you must look to
w[n*Omega] when Omega is the frequency
of the driving force and n a natural number.

Regards
Jens

gareth wrote:
> 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[=CE=B8[t]] + g Cos[wD t]
>
> Theta is the displacement, w the frequency, wD the driving frequency an=
d 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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