Mathematica 9 is now available
Services & Resources / Wolfram Forums
-----
 /
MathGroup Archive
2006
*January
*February
*March
*April
*May
*June
*July
*August
*September
*October
*November
*December
*Archive Index
*Ask about this page
*Print this page
*Give us feedback
*Sign up for the Wolfram Insider

MathGroup Archive 2006

[Date Index] [Thread Index] [Author Index]

Search the Archive

Problem solving equation using Solve

  • To: mathgroup at smc.vnet.net
  • Subject: [mg66153] Problem solving equation using Solve
  • From: "akil" <akomur at wanadoo.nl>
  • Date: Mon, 1 May 2006 01:30:45 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

I compute a derivative of a function od fime which contains the variables 
ax,ay,bx,by,cx,cy,centerOfMassx,centerOfMassy, beta and v.

These variables are all real numbers.

By doing

afgeleide =
FullSimplify[
D[Cones[beta, v],
v], {{ax, ay, bx, by, cx, cy, dx, dy, centerOfMassx,
centerOfMassy} \[Element] Reals}, TimeConstraint -> 5]

I get the following, for which I want to compute solutions = Solve[afgeleide 
== 0, v]

But the problem is that this is too hard for my pc to solve with 
mathematica, can anyone help me to change the function so that mathematica 
can handle it.

Any help appreciated.



\!\(\(afgeleide = \((\((\(-1\) + \((\((ax -
bx)\)\ centerOfMassx\ \((\(-cy\)\ dx +
centerOfMassy\ \((\(-cx\) + dx)\) +
centerOfMassx\ \((cy - dy)\) + cx\ dy)\)\ Sec[
beta]\ \((\((cy - dy)\)\ Cos[
beta] + \((\(-cx\) + dx)\)\ Sin[beta])\)\ Tan[
beta])\)/\((\((centerOfMassx\ cy - cy\ dx -
centerOfMassx\ dy +
cx\ dy + \((\(-cx\) + dx)\)\ \((centerOfMassx -
v)\)\ Tan[
beta])\)\ \((\(-cy\)\ \((\((\(-ax\) +
bx)\)\ centerOfMassy + \((ay -
by)\)\ \((centerOfMassx -
dx)\))\) + \((\((\(-ax\) +
bx)\)\ centerOfMassy + \((ay -
by)\)\ \((centerOfMassx -
cx)\))\)\ dy + \((ay\ \((cx -
dx)\)\ \((centerOfMassx - v)\) -
by\ \((cx - dx)\)\ \((centerOfMassx -
v)\) - \((ax -
bx)\)\ \((centerOfMassy\ cx -
centerOfMassy\ dx + cy\ dx - cx\ dy -
cy\ v + dy\ v)\))\)\ Tan[
beta])\))\) + \((\((centerOfMassy\ \((cx -
dx)\) + cy\ dx - cx\ dy +
centerOfMassx\ \((\(-cy\) +
dy)\))\)\ Sec[beta]\^2\ \((\((\(-cy\) +
dy)\)\ Cos[beta] + \((cx - dx)\)\ Sin[
beta])\)\ \((\((cy\ \((ax\ by\ centerOfMassx \
- ax\ by\ dx + ax\ centerOfMassy\ dx - bx\ centerOfMassy\ dx +
ay\ bx\ \((\(-centerOfMassx\) +
dx)\))\) + \((\(-ax\)\ by\ \
centerOfMassx + ay\ bx\ \((centerOfMassx - cx)\) + ax\ by\ cx -
ax\ centerOfMassy\ cx +
bx\ centerOfMassy\ cx)\)\ dy)\)\ Cos[
beta] + \((centerOfMassx\ \((\(-ax\)\ by\ cx \
+ ax\ by\ dx - ax\ cy\ dx + bx\ cy\ dx + \((ax - bx)\)\ cx\ dy)\) +
ay\ bx\ \((cx - dx)\)\ \((centerOfMassx -
v)\) + \((ax\ \((\((by -
centerOfMassy)\)\ \((cx - dx)\) +
centerOfMassx\ \((cy - dy)\))\) +
bx\ \((centerOfMassy\ cx -
centerOfMassx\ cy -
centerOfMassy\ dx +
centerOfMassx\ dy)\))\)\ v)\)\ Sin[
beta])\)\ Tan[
beta])\)/\((\((ax -
bx)\)\ \((cy\ dx - cx\ dy + centerOfMassx\ \
\((\(-cy\) + dy)\) + \((cx - dx)\)\ \((centerOfMassx - v)\)\ 
Tan[beta])\)\^3\ \
\((\(ay - by\)\/\(ax - bx\) + \(centerOfMassy\ \((cy - dy)\) + \((\(-cy\)\ 
dx \
+ centerOfMassy\ \((\(-cx\) + dx)\) + cx\ dy + cy\ v - dy\ v)\)\ \
Tan[beta]\)\/\(cy\ dx - cx\ dy + centerOfMassx\ \((\(-cy\) + dy)\) + \((cx - 
\
dx)\)\ \((centerOfMassx - v)\)\ \
Tan[beta]\))\)\^2)\))\)/\((\[Sqrt]\((\((\((\(-ax\)\ by\ centerOfMassx\ cy + 
\
ax\ by\ cy\ dx - ax\ centerOfMassy\ cy\ dx + bx\ centerOfMassy\ cy\ dx + ax\ 
\
by\ centerOfMassx\ dy - ax\ by\ cx\ dy + ax\ centerOfMassy\ cx\ dy - bx\ \
centerOfMassy\ cx\ dy + ay\ \((\(-cy\)\ dx + centerOfMassx\ \((cy - dy)\) + 
\
cx\ dy)\)\ \((bx - v)\) + \((\((ax - bx)\)\ centerOfMassy\ \((cy - dy)\) + 
by\
\ \((centerOfMassx\ cy - cy\ dx - centerOfMassx\ dy + cx\ dy)\))\)\ v + \
\((centerOfMassx - v)\)\ \((\(-ay\)\ bx\ cx + ax\ by\ cx + ay\ bx\ dx - ax\ 
\
by\ dx + ax\ cy\ dx - bx\ cy\ dx - ax\ cx\ dy + bx\ cx\ dy + \((\((ay - 
by)\)\
\ \((cx - dx)\) - \((ax - bx)\)\ \((cy - dy)\))\)\ v)\)\ Tan[beta])\)\^2 + \
\((centerOfMassy\ \((ay\ \((\(-cy\)\ dx + bx\ \((cy - dy)\) + cx\ dy)\) + 
by\ \
\((cy\ dx - cx\ dy + ax\ \((\(-cy\) + dy)\))\))\) + \((ay\ \((\(-bx\)\ \
centerOfMassy\ cx + bx\ centerOfMassy\ dx - bx\ cy\ dx + centerOfMassx\ cy\ 
\
dx + bx\ cx\ dy - centerOfMassx\ cx\ dy + \((centerOfMassy\ \((cx - dx)\) + 
\
\((bx - centerOfMassx)\)\ \((cy - dy)\))\)\ v)\) + by\ \((centerOfMassy\ \
\((\(-cx\) + dx)\)\ v + centerOfMassx\ \((\(-cy\)\ dx + cx\ dy + cy\ v - dy\ 
\
v)\) + ax\ \((centerOfMassy\ \((cx - dx)\) + cy\ dx - cx\ dy - cy\ v + dy\ 
v)\
\))\))\)\ Tan[beta])\)\^2)\)/\((cy\ \((\((\(-ax\) + bx)\)\ centerOfMassy + \
\((ay - by)\)\ \((centerOfMassx - dx)\))\) - \((\((\(-ax\) + bx)\)\ \
centerOfMassy + \((ay - by)\)\ \((centerOfMassx - cx)\))\)\ dy + \((\(-ay\)\ 
\
\((cx - dx)\)\ \((centerOfMassx - v)\) + by\ \((cx - dx)\)\ \((centerOfMassx 
\
- v)\) + \((ax - bx)\)\ \((centerOfMassy\ cx - centerOfMassy\ dx + cy\ dx - 
\
cx\ dy - cy\ v + dy\ v)\))\)\ Tan[beta])\)\^2)\))\) - \((\((ax\ by\ \
centerOfMassx\ cy - ax\ by\ cy\ dx + ax\ centerOfMassy\ cy\ dx -
bx\ centerOfMassy\ cy\ dx - ax\ by\ centerOfMassx\ dy +
ax\ by\ cx\ dy - ax\ centerOfMassy\ cx\ dy +
bx\ centerOfMassy\ cx\ dy +
ay\ \((cy\ dx - cx\ dy +
centerOfMassx\ \((\(-cy\) + dy)\))\)\ \((bx -
v)\) - \((\((ax - bx)\)\ centerOfMassy\ \((cy -
dy)\) +
by\ \((centerOfMassx\ cy - cy\ dx -
centerOfMassx\ dy +
cx\ dy)\))\)\ v + \((centerOfMassx -
v)\)\ \((\(-ax\)\ by\ cx + ax\ by\ dx -
ax\ cy\ dx + bx\ cy\ dx + ax\ cx\ dy -
bx\ cx\ dy +
ay\ \((cx - dx)\)\ \((bx -
v)\) + \((by\ \((cx - dx)\) + \((ax -
bx)\)\ \((cy - dy)\))\)\ v)\)\ Tan[
beta])\)\ \((\((2\ \((ay -
by)\)\ \((ay\ \((bx - centerOfMassx)\) +
by\ centerOfMassx - bx\ centerOfMassy +
ax\ \((\(-by\) +
centerOfMassy)\))\)\ \((\(-cy\)\ dx +
centerOfMassy\ \((\(-cx\) + dx)\) +
centerOfMassx\ \((cy - dy)\) +
cx\ dy)\)\ Sec[beta]\^2\ \((\((\(-cy\) +
dy)\)\ Cos[beta] + \((cx - dx)\)\ Sin[
beta])\)\ \((centerOfMassy\ \((by\ \
\((\(-cy\)\ dx + ax\ \((cy - dy)\) + cx\ dy)\) +
ay\ \((cy\ dx - cx\ dy +
bx\ \((\(-cy\) + dy)\))\))\)\ Cos[
beta] + \((by\ \((\(-ax\)\ centerOfMassy\ \
cx + ax\ centerOfMassy\ dx - ax\ cy\ dx + centerOfMassx\ cy\ dx +
ax\ cx\ dy -
centerOfMassx\ cx\ dy + \
\((centerOfMassy\ \((cx - dx)\) + \((ax - centerOfMassx)\)\ \((cy -
dy)\))\)\ v)\) +
ay\ \((centerOfMassy\ \((\(-cx\) +
dx)\)\ v +
centerOfMassx\ \((\(-cy\)\ dx +
cx\ dy + cy\ v - dy\ v)\) +
bx\ \((centerOfMassy\ \((cx - dx)\) +
cy\ dx - cx\ dy - cy\ v +
dy\ v)\))\))\)\ Sin[beta])\)\ Tan[
beta])\)/\((cy\ \((\((\(-ax\) + bx)\)\ \
centerOfMassy + \((ay - by)\)\ \((centerOfMassx - dx)\))\) - \((\((\(-ax\) + 
\
bx)\)\ centerOfMassy + \((ay - by)\)\ \((centerOfMassx - cx)\))\)\ dy + \
\((\(-ay\)\ \((cx - dx)\)\ \((centerOfMassx - v)\) + by\ \((cx - dx)\)\ \
\((centerOfMassx - v)\) + \((ax - bx)\)\ \((centerOfMassy\ cx - 
centerOfMassy\
\ dx + cy\ dx - cx\ dy - cy\ v + dy\ v)\))\)\ Tan[beta])\)\^3 + \((2\ \((ax\ 
\
by\ centerOfMassx\ cy - ax\ by\ cy\ dx + ax\ centerOfMassy\ cy\ dx -
bx\ centerOfMassy\ cy\ dx -
ax\ by\ centerOfMassx\ dy + ax\ by\ cx\ dy -
ax\ centerOfMassy\ cx\ dy +
bx\ centerOfMassy\ cx\ dy +
ay\ \((cy\ dx - cx\ dy +
centerOfMassx\ \((\(-cy\) +
dy)\))\)\ \((bx -
v)\) - \((\((ax -
bx)\)\ centerOfMassy\ \((cy - dy)\) +
by\ \((centerOfMassx\ cy - cy\ dx -
centerOfMassx\ dy +
cx\ dy)\))\)\ v + \((centerOfMassx -
v)\)\ \((\(-ax\)\ by\ cx + ax\ by\ dx -
ax\ cy\ dx + bx\ cy\ dx + ax\ cx\ dy -
bx\ cx\ dy +
ay\ \((cx - dx)\)\ \((bx -
v)\) + \((by\ \((cx - dx)\) + \((ax -
bx)\)\ \((cy - dy)\))\)\ v)\)\ Tan[
beta])\)\ \((\(-1\) + \((\((ax -
bx)\)\ centerOfMassx\ \((\(-cy\)\ dx \
+ centerOfMassy\ \((\(-cx\) + dx)\) + centerOfMassx\ \((cy - dy)\) +
cx\ dy)\)\ Sec[
beta]\ \((\((cy - dy)\)\ Cos[
beta] + \((\(-cx\) + dx)\)\ Sin[
beta])\)\ Tan[
beta])\)/\((\((centerOfMassx\ cy -
cy\ dx - centerOfMassx\ dy +
cx\ dy + \((\(-cx\) +
dx)\)\ \((centerOfMassx - v)\)\ Tan[
beta])\)\ \((\(-cy\)\ \((\((\(-ax\) +
bx)\)\ centerOfMassy + \((ay -
by)\)\ \((centerOfMassx -
dx)\))\) + \((\((\(-ax\) +
bx)\)\ centerOfMassy + \((ay -
by)\)\ \((centerOfMassx -
cx)\))\)\ dy + \((ay\ \((cx -
dx)\)\ \((centerOfMassx - v)\) -
by\ \((cx - dx)\)\ \((centerOfMassx -
v)\) - \((ax -
bx)\)\ \((centerOfMassy\ cx -
centerOfMassy\ dx + cy\ dx - cx\ dy -
cy\ v + dy\ v)\))\)\ Tan[
beta])\))\) + \((\((centerOfMassy\ \
\((cx - dx)\) + cy\ dx - cx\ dy + centerOfMassx\ \((\(-cy\) +
dy)\))\)\ Sec[beta]\^2\ \((\((\(-cy\) \
+ dy)\)\ Cos[beta] + \((cx -
dx)\)\ Sin[
beta])\)\ \((\((cy\ \((ax\ by\ \
centerOfMassx - ax\ by\ dx + ax\ centerOfMassy\ dx - bx\ centerOfMassy\ dx +
ay\ bx\ \((\(-centerOfMassx\) +
dx)\))\) + \((\(-ax\)\ by\ \
centerOfMassx + ay\ bx\ \((centerOfMassx - cx)\) + ax\ by\ cx -
ax\ centerOfMassy\ cx +
bx\ centerOfMassy\ cx)\)\ dy)\)\ Cos[
beta] + \((centerOfMassx\ \((\(-ax\)\ \
by\ cx + ax\ by\ dx - ax\ cy\ dx + bx\ cy\ dx + \((ax - bx)\)\ cx\ dy)\) +
ay\ bx\ \((cx -
dx)\)\ \((centerOfMassx -
v)\) + \((ax\ \((\((by -
centerOfMassy)\)\ \((cx - dx)\) +
centerOfMassx\ \((cy - dy)\))\) +
bx\ \((centerOfMassy\ cx -
centerOfMassx\ cy -
centerOfMassy\ dx +
centerOfMassx\ dy)\))\)\ v)\)\ Sin[
beta])\)\ Tan[
beta])\)/\((\((ax -
bx)\)\ \((cy\ dx - cx\ dy + \
centerOfMassx\ \((\(-cy\) + dy)\) + \((cx - dx)\)\ \((centerOfMassx - v)\)\ 
\
Tan[beta])\)\^3\ \((\(ay - by\)\/\(ax - bx\) + \(centerOfMassy\ \((cy - 
dy)\) \
+ \((\(-cy\)\ dx + centerOfMassy\ \((\(-cx\) + dx)\) + cx\ dy + cy\ v - dy\ 
\
v)\)\ Tan[beta]\)\/\(cy\ dx - cx\ dy + centerOfMassx\ \((\(-cy\) + dy)\) + \
\((cx - dx)\)\ \((centerOfMassx - v)\)\ 
Tan[beta]\))\)\^2)\))\))\)/\((\(-cy\)\
\ \((\((\(-ax\) + bx)\)\ centerOfMassy + \((ay - by)\)\ \((centerOfMassx -
dx)\))\) + \((\((\(-ax\) +
bx)\)\ centerOfMassy + \((ay -
by)\)\ \((centerOfMassx -
cx)\))\)\ dy + \((ay\ \((cx -
dx)\)\ \((centerOfMassx - v)\) -
by\ \((cx - dx)\)\ \((centerOfMassx -
v)\) - \((ax -
bx)\)\ \((centerOfMassy\ cx -
centerOfMassy\ dx + cy\ dx - cx\ dy -
cy\ v + dy\ v)\))\)\ Tan[
beta])\))\))\)/\((2\ \((\(-cy\)\ \
\((\((\(-ax\) + bx)\)\ centerOfMassy + \((ay - by)\)\ \((centerOfMassx -
dx)\))\) + \((\((\(-ax\) +
bx)\)\ centerOfMassy + \((ay -
by)\)\ \((centerOfMassx -
cx)\))\)\ dy + \((ay\ \((cx -
dx)\)\ \((centerOfMassx - v)\) -
by\ \((cx - dx)\)\ \((centerOfMassx -
v)\) - \((ax -
bx)\)\ \((centerOfMassy\ cx -
centerOfMassy\ dx + cy\ dx - cx\ dy -
cy\ v + dy\ v)\))\)\ Tan[
beta])\)\ \((\((\((\(-ax\)\ by\ centerOfMassx\ cy + \
ax\ by\ cy\ dx - ax\ centerOfMassy\ cy\ dx + bx\ centerOfMassy\ cy\ dx + ax\ 
\
by\ centerOfMassx\ dy - ax\ by\ cx\ dy + ax\ centerOfMassy\ cx\ dy - bx\ \
centerOfMassy\ cx\ dy + ay\ \((\(-cy\)\ dx + centerOfMassx\ \((cy - dy)\) + 
\
cx\ dy)\)\ \((bx - v)\) + \((\((ax - bx)\)\ centerOfMassy\ \((cy - dy)\) + 
by\
\ \((centerOfMassx\ cy - cy\ dx - centerOfMassx\ dy + cx\ dy)\))\)\ v + \
\((centerOfMassx - v)\)\ \((\(-ay\)\ bx\ cx + ax\ by\ cx + ay\ bx\ dx - ax\ 
\
by\ dx + ax\ cy\ dx - bx\ cy\ dx - ax\ cx\ dy + bx\ cx\ dy + \((\((ay - 
by)\)\
\ \((cx - dx)\) - \((ax - bx)\)\ \((cy - dy)\))\)\ v)\)\ Tan[beta])\)\^2 + \
\((centerOfMassy\ \((ay\ \((\(-cy\)\ dx + bx\ \((cy - dy)\) + cx\ dy)\) + 
by\ \
\((cy\ dx - cx\ dy + ax\ \((\(-cy\) + dy)\))\))\) + \((ay\ \((\(-bx\)\ \
centerOfMassy\ cx + bx\ centerOfMassy\ dx - bx\ cy\ dx + centerOfMassx\ cy\ 
\
dx + bx\ cx\ dy - centerOfMassx\ cx\ dy + \((centerOfMassy\ \((cx - dx)\) + 
\
\((bx - centerOfMassx)\)\ \((cy - dy)\))\)\ v)\) + by\ \((centerOfMassy\ \
\((\(-cx\) + dx)\)\ v + centerOfMassx\ \((\(-cy\)\ dx + cx\ dy + cy\ v - dy\ 
\
v)\) + ax\ \((centerOfMassy\ \((cx - dx)\) + cy\ dx - cx\ dy - cy\ v + dy\ 
v)\
\))\))\)\ Tan[beta])\)\^2)\)/\((cy\ \((\((\(-ax\) + bx)\)\ centerOfMassy + \
\((ay - by)\)\ \((centerOfMassx - dx)\))\) - \((\((\(-ax\) + bx)\)\ \
centerOfMassy + \((ay - by)\)\ \((centerOfMassx - cx)\))\)\ dy + \((\(-ay\)\ 
\
\((cx - dx)\)\ \((centerOfMassx - v)\) + by\ \((cx - dx)\)\ \((centerOfMassx 
\
- v)\) + \((ax - bx)\)\ \((centerOfMassy\ cx - centerOfMassy\ dx + cy\ dx - 
\
cx\ dy - cy\ v + dy\ v)\))\)\ \
Tan[beta])\)\^2)\)\^\(3/2\))\))\)/\((\[Sqrt]\((1 - \((\(-ax\)\ by\ \
centerOfMassx\ cy + ax\ by\ cy\ dx - ax\ centerOfMassy\ cy\ dx + bx\ \
centerOfMassy\ cy\ dx + ax\ by\ centerOfMassx\ dy - ax\ by\ cx\ dy + ax\ \
centerOfMassy\ cx\ dy - bx\ centerOfMassy\ cx\ dy + ay\ \((\(-cy\)\ dx + \
centerOfMassx\ \((cy - dy)\) + cx\ dy)\)\ \((bx - v)\) + \((\((ax - bx)\)\ \
centerOfMassy\ \((cy - dy)\) + by\ \((centerOfMassx\ cy - cy\ dx - \
centerOfMassx\ dy + cx\ dy)\))\)\ v + \((centerOfMassx - v)\)\ \((\(-ay\)\ 
bx\
\ cx + ax\ by\ cx + ay\ bx\ dx - ax\ by\ dx + ax\ cy\ dx - bx\ cy\ dx - ax\ 
\
cx\ dy + bx\ cx\ dy + \((\((ay - by)\)\ \((cx - dx)\) - \((ax - bx)\)\ \((cy 
\
- dy)\))\)\ v)\)\ Tan[beta])\)\^2/\((\((\(-ax\)\ by\ centerOfMassx\ cy + ax\ 
\
by\ cy\ dx - ax\ centerOfMassy\ cy\ dx + bx\ centerOfMassy\ cy\ dx + ax\ by\ 
\
centerOfMassx\ dy - ax\ by\ cx\ dy + ax\ centerOfMassy\ cx\ dy - bx\ \
centerOfMassy\ cx\ dy + ay\ \((\(-cy\)\ dx + centerOfMassx\ \((cy - dy)\) + 
\
cx\ dy)\)\ \((bx - v)\) + \((\((ax - bx)\)\ centerOfMassy\ \((cy - dy)\) + 
by\
\ \((centerOfMassx\ cy - cy\ dx - centerOfMassx\ dy + cx\ dy)\))\)\ v + \
\((centerOfMassx - v)\)\ \((\(-ay\)\ bx\ cx + ax\ by\ cx + ay\ bx\ dx - ax\ 
\
by\ dx + ax\ cy\ dx - bx\ cy\ dx - ax\ cx\ dy + bx\ cx\ dy + \((\((ay - 
by)\)\
\ \((cx - dx)\) - \((ax - bx)\)\ \((cy - dy)\))\)\ v)\)\ Tan[beta])\)\^2 + \
\((centerOfMassy\ \((ay\ \((\(-cy\)\ dx + bx\ \((cy - dy)\) + cx\ dy)\) + 
by\ \
\((cy\ dx - cx\ dy + ax\ \((\(-cy\) + dy)\))\))\) + \((ay\ \((\(-bx\)\ \
centerOfMassy\ cx + bx\ centerOfMassy\ dx - bx\ cy\ dx + centerOfMassx\ cy\ 
\
dx + bx\ cx\ dy - centerOfMassx\ cx\ dy + \((centerOfMassy\ \((cx - dx)\) + 
\
\((bx - centerOfMassx)\)\ \((cy - dy)\))\)\ v)\) + by\ \((centerOfMassy\ \
\((\(-cx\) + dx)\)\ v + centerOfMassx\ \((\(-cy\)\ dx + cx\ dy + cy\ v - dy\ 
\
v)\) + ax\ \((centerOfMassy\ \((cx - dx)\) + cy\ dx - cx\ dy - cy\ v + dy\ 
v)\
\))\))\)\ Tan[beta])\)\^2)\))\))\);\)\[IndentingNewLine]
solutions\ = \ Solve[afgeleide\ == \ 0, v]\)



Akil

akil39 at gmail.com



  • Prev by Date: Re: Solving Nonlinear Transcedental equations
  • Next by Date: Re: Apparent accuracy error in least squares fit
  • Previous by thread: Re: Solving Nonlinear Transcedental equations
  • Next by thread: Re: 3D plot with range restricted to non-rectangular region