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

**References**:**newbie: explicit function works, "function object" doesn't***From:*Tom Roche <tlroche@gmail.com>