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MathGroup Archive 2006

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Re: Problems solving using Solve

  • To: mathgroup at smc.vnet.net
  • Subject: [mg68829] Re: Problems solving using Solve
  • From: "akil" <akomur at wanadoo.nl>
  • Date: Sun, 20 Aug 2006 04:43:49 -0400 (EDT)
  • References: <ec65bn$1f8$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

definition for cd is cd[input_,rcCD_,cx_,cy_] := rcCD*input + cy - rcCD*cx; 
(which just defines a line of the form y=ax+b)

Using NSolve instead of Solve still takes way too long (quit it after 15 
minutes, do not know if it even will solve it). I have about a 100 cones for 
each part I need to test and the way it is now takes too long.

In my usage all values except beta and v are Reals. Beta is usually the 
range [0, Pi/2] and v is also a Real.

For a solvable solution try:

{ax,ay}= {7,4} and {cx,cy}= {21,11} and
{centerOfMassx,centerOfMassy}={13,7} and rcAB=3 and
rcCD=7/4

That should give a solution, and quite fast at that.

Akil

"akil" <akomur at wanadoo.nl> schreef in bericht 
news:ec65bn$1f8$1 at smc.vnet.net...
>I have a problem suing the following code:
>
> Cone[beta_, v_,rcAB_,rcCD_,ax_,ay_,cx_,cy_,centerOfMassx_,centerOfMassy_] 
> :=
> Module[
> {betaUsed, vtemp, fx, fy, ex, ey,
> waarde,criticalRC,criticalHeight,xVerplaatsing,ePx2Py2},
>      betaUsed = beta ;
>      vtemp = v;
>      fline[x_] := Tan[betaUsed]x - Tan[betaUsed]vtemp;
>      fx = x /. Solve[fline[x] == cd[x,rcCD,cx,cy], x][[1]];
>      fy = cd[fx,rcCD,cx,cy];
>      criticalRC = (centerOfMassy - fy)/(centerOfMassx - fx);
>      criticalHeight = -criticalRC*fx + fy;
>      ex = (-ay + rcAB*ax + criticalHeight)/(rcAB + (-criticalRC));
>      ey = ab[ex,rcAB,ax,ay];
>      xVerplaatsing = ex - vtemp;
>      ePx2Py2 = Sqrt[xVerplaatsing^2 + ey^2];
>      waarde = xVerplaatsing/ePx2Py2;
>      ArcCos[-waarde]
> ];
>
> afg =
> Simplify[D[Cone[beta,v,rcAB,rcCD,ax,ay,cx,cy,centerOfMassx,centerOfMassy],v],
> TimeConstraint -> 1 ];
> Solve[afg== 0, v];
>
> eg.
> {ax,ay}= {-44.9376, 36.1678} and {cx,cy}= {17.8329, 122.477} and
> {centerOfMassx,centerOfMassy}={-18.6338,72.3356} and rcAB=-0.166667 and
> rcCD=-0.37931
>
> Doing the Solve[afg== 0, v] takes ages (after an hour I quit it). Is there
> any way I can make it work faster? Is any code in Cone such that it
> unnecessarily makes it run faster? So are there any ways I can try to make
> everything run faster? Using integers it runs, but it takes too long when
> using real cones (made up of four points A B C D and a centerOfMass).
>
> Akil
>
> 



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