       Re: Mathematica can't win against Tiger Woods

• To: mathgroup at smc.vnet.net
• Subject: [mg19692] Re: Mathematica can't win against Tiger Woods
• From: weber at math.uni-bonn.de (Matthias Weber)
• Date: Sat, 11 Sep 1999 16:36:01 -0400
• Organization: RHRZ - University of Bonn (Germany)
• References: <7r7jvo\$ck4@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```In article <7r7jvo\$ck4 at smc.vnet.net>, "William M. MacDonald"
<wm2 at umail.umd.edu> wrote:

> I want to use the study of golf drives in teaching theoretical methods.  An
> approximate pair of equations to get insight assumes that the drag force is
>  dependence.  The equations for a ball with backspin to provide lift are
>      x''[t]== - (a x'[t]+b y'[t]),
>      y''[t]== - g - (a y'[t]- b x'[t])
>  Mathematica returns a very complicated and apparently complex expression in
>  about 9 seconds on my 250 MHz G3 Powerbook.  Simplify takes 1min and 20
>  seconds and still returns an apparently complex expression.  If I apply
>  FullSimplify on the solution for say x[t], I get no answer in 6 minutes.
>
>      I have a PC version of another system that I can run on my
Powerbook using
>  Virtual PC.  It requires 6 seconds to deliver a lengthy but obviously real,
>  no Exp[(a+ I b)t] terms or (a + I b)(a - I b) terms.
>
>      I have never been able to learn why Mathematica is so slow in solving
>  coupled equations and returns (as USUAL unless you use Simplify) such
>  inelegant results.  Is there any computer algebra NERD out
>  there who knows the answer.  (Don't tell me to use AlgebraicManipulation; I
>  am trying to sell Mathematica to users who don't want to spend time
> learning
>  fancy tricks.)
>

{(a^4*C + a^3*C + a*b*(-2*g + b*C) +
b^3*(g*t + b*C - C) +
a^2*b*(g*t + 2*b*C - C) -
((a^2 + b^2)*((a*C - b*C)*Cos[b*t] -
(b*C + a*C)*Sin[b*t]))/E^(a*t))/
(a^2 + b^2)^2, (a^4*C +
b^2*(-g + b*(b*C + C)) +
a^2*(g + b*(2*b*C + C)) + a^3*(-(g*t) + C) +
a*b^2*(-(g*t) + C) -
((a^2 + b^2)*((b*C + a*C)*Cos[b*t] +
(a*C - b*C)*Sin[b*t]))/E^(a*t))/(a^2 + b^2)^2
}

with Mathematica 3.0, using just

DSolve[{x''[t]== - (a x'[t]+b y'[t]),
y''[t]== - g - (a y'[t]- b x'[t])},{x,y},t];

{x[t],y[t]}/.%[];

Simplify[%];

FullSimplify[%]

Takes about 2 minutes in total. On a Mac. No fancy tricks.
Of course there are always examples where system X will be better
than system Y. The real trouble is caused not by the better features
of system Y, but by the bugs of system X.

Best,
Matthias

```

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