Re: [Phys-l] solving an energy equation

[Carl Mungan <mungan@usna.edu>]

Thanks to John Denker for such a clear exposition. Very helpful.

In my case, we have V as a function of y, so it's known at all 
points. We conclude that we know all we need to know, indeed. So why 
can't Mathematica "figure out" how to do the numerical timestepping? 
In other words, why can't it do whatever derivatives it needs to 
solve the following problem?

It complains about the following:

f[t] := (x'[t])^2 == 1 - 2x[t]
g[t] := D[f[t], t]

sol1 = NDSolve[{f[t], x[0] == 0}, x, {t, 0, 2}]
Plot[x[t] /. sol1, {t, 0, 2}]

but is perfectly happy with the following, even though I'm not 
supplying any new information:

sol2 = NDSolve[{g[t], x[0] == 0, x'[0] == 1}, x, {t, 0, 2}]
Plot[x[t] /. sol2, {t, 0, 2}]

This appears to me to be some sort of defect in the way Mathematica 
is coded. Or am I missing something?
--
Carl E. Mungan, Asst Prof of Physics  410-293-6680 (O) -3729 (F)
Naval Academy Stop 9c, 572C Holloway Rd, Annapolis MD 21402-5002
mailto:mungan@usna.edu     http://usna.edu/Users/physics/mungan/