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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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