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

*To*: mathgroup at smc.vnet.net*Subject*: [mg96267] Re: [mg96207] newbie: explicit function works, "function object" doesn't*From*: "David Park" <djmpark at comcast.net>*Date*: Tue, 10 Feb 2009 05:54:28 -0500 (EST)*References*: <32689826.1234178726482.JavaMail.root@m02>

Tom, It is generally good practice to have ALL symbols in a function definition be part of the definition itself and not just 'hanging loose'. This made a difference in the Manipulate statement because the control parameters are local variables within the Manipulate statement. That is why it would not work for you until you put the definitions and solution inside the Manipulate statement. First solve the differential equation and obtain a function for theta that contains the parameters in the definition of the function. In this case the parameters are entered as what are called SubVaues in Mathematica. You could remove the semicolons to see the intermediate steps. Clear[theta]; linearPendulum = {theta''[t] == -omega^2 theta[t]}; Part[DSolve[{linearPendulum, theta'[0] == v0, theta[0] == theta0}, theta, t], 1, 1]; theta[omega_, theta0_, v0_][t_] = theta[t] /. % (omega theta0 Cos[omega t] + v0 Sin[omega t])/omega We can see that we now have a way to express the function with any particular set of parameters. theta[2, 3, 1][t] 1/2 (6 Cos[2 t] + Sin[2 t]) Now the Manipulate statement is much simpler. All we need is the Plot statement. Dynamic plots like this are much better if they are displayed with a fixed PlotRange. However, you might want to add an additional control to set the vertical plot range. Manipulate[ Plot[theta[omega, theta0, v0][t], {t, -2 \[Pi], 2 \[Pi]}, Frame -> True, AxesStyle -> LightGray, PlotRange -> {{-2 \[Pi], 2 \[Pi]}, {-5, 5}}], {{omega, 1}, 0.0001, 5, Appearance -> "Labeled"}, {{theta0, 1}, 0, 5, Appearance -> "Labeled"}, {{v0, 1}, 0, 5, Appearance -> "Labeled"}] Now you should be able to do the damped oscillator. David Park djmpark at comcast.net http://home.comcast.net/~djmpark/ From: Tom Roche [mailto:tlroche at gmail.com] 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>