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Re: Can DSolve handle normalized vectors?
*To*: mathgroup at smc.vnet.net
*Subject*: [mg83556] Re: Can DSolve handle normalized vectors?
*From*: dh <dh at metrohm.ch>
*Date*: Thu, 22 Nov 2007 06:38:52 -0500 (EST)
*References*: <fi0otp$65a$1@smc.vnet.net>
Hi,
I wrote your system of equations in a more approbriate form and DSolve
has no problem:
{xx1,xx2}={100000000000,0};
f1[t_]=(6.673`*^31 (-x1[t]+xx1))/((-x1[t]+xx1)^2+(-x2[t]+xx2)^2);
f2[t_]=(6.673`*^31 (-x2[t]+xx2))/((-x1[t]+xx1)^2+(-x2[t]+xx2)^2);
eqs={x1[0]==0,x2[0]==0,
x1'[0]==0,x2'[0]==100000000000000000,
x1''[t]==f1[t]/1000000000000000000,x2''[t]==f2[t]/1000000000000000000}
NDSolve[eqs,{x1[t],x2[t]},{t,0,1}]
It is a good idea to choose units so that you have numerical factors of
the order of unity. Otherwise you may have numerical problems.
hope this helps, Daniel
ram.rachum at gmail.com wrote:
> Hello hello, it's me again. So I figured out how to use vectors in
> DSolve. Now I tried to input a simple physical system into DSolve. The
> only physical force I allowed was gravity. It didn't work. I tried
> various systems, but none of them worked. I gradually simplified them,
> making one of the objects stationary, playing with the force
> equations, etc. I think I narrowed down the problem: DSolve won't work
> if there I use a unit vector in one of the functions.
> I defined a function unitvector[x] that gives you a vector in the
> direction of x with a length of one. It's quite straightforward, but
> when I use this function in one of the equations, DSolve goes
> Solve::svars. I tried calculating a unit vector in other ways, without
> calling the function, but they all produced the same svars.
> Here's the code:
>
> \!\(\(x[t_] = {x1[t], x2[t]};\)\[IndentingNewLine]
> \(xx[t_] = {xx1[t], xx2[t]};\)\[IndentingNewLine]
> \(f[t_] = {f1[t], f2[t]};\)\[IndentingNewLine]
> \(ff[t_] = {ff1[t], ff2[t]};\)\[IndentingNewLine]
> \(g = 6.673*10\^\(-11\);\)\[IndentingNewLine]
> \(vnorm[x_] := \@\((x . x)\);\)\[IndentingNewLine]
> unitvector[x_] := x/vnorm[x]\)
>
> \!\(eqn = {x[0] == {
> 0, 0}, \(x'\)[0] == {0, 10\^17},
> xx[t] == {10\^11, 0}, \(x''\)[t] == f[t]/\((\ 1*10\^18)\),
> f[t] == \(g*\((1*10\^18)\)*\((1*10\^24)\)\)\/vnorm[xx[t] -
> x[t]]*
> unitvector[xx[t] - x[t]]}\)
>
> DSolve[Thread /@ eqn // Flatten, Flatten[{x[t], xx[t], f[t]}], {t}]
>
> So is Mathematica simply unable to solve something that uses a unit
> vector?
>
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