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Re: newbie: explicit function works, "function object" doesn't

  • To: mathgroup at smc.vnet.net
  • Subject: [mg96231] Re: newbie: explicit function works, "function object" doesn't
  • From: dh <dh at metrohm.com>
  • Date: Tue, 10 Feb 2009 05:47:47 -0500 (EST)
  • References: <gmp0st$c30$1@smc.vnet.net>


Hi Tom,

define a function with all your parameters and use it inside Manipulate:

linearPendulum = {theta''[t] == -omega^2 theta[t]};

soln = DSolve[{linearPendulum, theta'[0] == v0, theta[0] == theta0},

    theta[t], t];

fun[t_, omega_, theta0_, v0_] = theta[t] /. soln[[1]];

Manipulate[(Plot[

    fun[t, omega, theta0, v0], {t, -2 Pi, 2 Pi}]), {{omega, 1}, 0,

   5}, {{theta0, 1}, 0, 5}, {{v0, 1}, 0, 5}]



hope this helps, Daniel



Tom Roche wrote:

> summary: I've got a function that I can Manipulate, but I can't

> Manipulate the things to which the function is assigned. I'm assuming

> this is due to a syntax error.

> 

> details:

> 

> As advertised by the Subject:, I'm new to Mathematica (specifically M7

> running on a linux cluster) so please excuse any lapses in

> terminology. I'd also appreciate pointers to specific docs rather than

> just an RTFM. Also feel free to refer to my notebook @

> 

> http://www.unc.edu/~tr/classes/GEOL861/hw1Notebook.nb

> 

> I'm trying initially to model a linearized pendulum

> 

> theta''[t] == -omega^2 theta[t]

> 

> (where omega=g/l) with the simple initial conditions

> 

> theta'[0]==v0

> theta[0]==theta0

> 

> Using

> 

> soln = DSolve[{linearPendulum, theta'[0] == v0, theta[0] == theta0},

> theta[t], t]

> 

> I get the solution

> 

> theta[t] -> (omega*theta0*Cos(omega*t) + (v0*Sin(omega*t)))/omega

> 

> However, when I try to Manipulate[Plot[soln...]], I get ... nothing.

> Not an error, and I do get the appropriate UI, but I don't get a plot.

> 

>>From what I've read, it seems Manipulate wants an expression like the

> RHS of 'soln', which I'll refer to here as a "function." (Please

> correct my usage as needed.) I got a "function object" with ReplaceAll

> 

> happysoln[t_] = theta[t] /. soln[[1]]

> 

> similar to a working example I've seen. But

> Manipulate[Plot[happysoln...]] also fails silently, like the previous.

> 

> However, when I manipulate the "function" directly

> 

> Manipulate[Plot[(omega theta0 Cos[omega t] + v0 Sin[omega t])/omega,

> {t, -2 Pi, 2 Pi}], {{omega, 1}, 0, 5}, {{theta0, 1}, 0, 5}, {{v0, 1},

> 0, 5}]

> 

> it works as designed: I get the UI with the plot, which I can twiddle

> with the sliders.

> 

> Why can I Manipulate the function, but not the containers of the

> function (i.e. soln, happysoln)? More importantly, with what syntax

> can I Manipulate those containers?

> 

> TIA, Tom Roche <Tom_Roche at pobox.com>

> 




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