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

• To: mathgroup at smc.vnet.net
• Subject: [mg96207] newbie: explicit function works, "function object" doesn't
• From: Tom Roche <tlroche at gmail.com>
• Date: Mon, 9 Feb 2009 05:35:29 -0500 (EST)

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>

• Follow-Ups:
  • Re: newbie: explicit function works, "function object"
    • From: Murray Eisenberg <murray@math.umass.edu>