Re: NDSolve solutions

• To: mathgroup at smc.vnet.net
• Subject: [mg125087] Re: NDSolve solutions
• From: Niles <niels.martinsen at gmail.com>
• Date: Tue, 21 Feb 2012 06:10:57 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <jhsto5\$nht\$1@smc.vnet.net>

```On Feb 20, 8:46 am, Niles <niels.martin... at gmail.com> wrote:
> Hi
>
> I have solved an ODE using NDSolve, and I plot the solution like this:
>
> ParametricPlot[{z[t], z'[t]} /. solution, {t, 0, 2 maxTime}, PlotRange
> -> {{0, 0.2}, {0, 450}}, AspectRatio -> 0.75]
>
> The curve shown (the velocity as a function of position) I want to use
> in a new mathematical expression. How can I do that? If I use z'[t],
> then it is as a function of time, which is no good to me.
>
>
> Best regards,
> Niles.

To clarify, what I have is a system of ODEs of the form

dx/dt = v
dv/dt = a = C*f(x),

where C denotes a constant and f(x) is some function of x. This system
is easy to solve using e.g.

NDSolve[x''[t] == -C*f(x), x[0] == 0, x'[0] == 0}, x, {t, 0, tMax}];

The solution x[t] (or rather, its derivative x'[t]) I need to use in
the following expression:

B(x) = A + v(x)

where A denotes a constant and v(x) is the velocity as a function of
position x. But please note that v is as a function of x, not t. What
should I do to achieve this?

Best regards,
Niles.

```

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