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Re: newbie: explicit function works, "function object"

  • To: mathgroup at smc.vnet.net
  • Subject: [mg96272] Re: [mg96207] newbie: explicit function works, "function object"
  • From: Murray Eisenberg <murray at math.umass.edu>
  • Date: Tue, 10 Feb 2009 05:55:22 -0500 (EST)
  • Organization: Mathematics & Statistics, Univ. of Mass./Amherst
  • References: <200902091035.FAA12396@smc.vnet.net>
  • Reply-to: murray at math.umass.edu

Perhaps you have in mind the result of something like the following?

Manipulate[
   Plot[
     Evaluate[
       theta[t]/.First@NDSolve[
         {theta''[t]==-omega^2 theta[t],theta'[0]==v0,theta[0]==theta0},
         theta[t],{t,0,10}]
     ],
   {t,0,10}],
{omega,0.1,5},{theta0,0,Pi/4},{v0,0,2}
]

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>
> 

-- 
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305


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