       Re: Mathematica can't win against Tiger Woods

• To: mathgroup at smc.vnet.net
• Subject: [mg19686] Re: Mathematica can't win against Tiger Woods
• From: "Kevin J. McCann" <kevinmccann at Home.com>
• Date: Sat, 11 Sep 1999 16:35:58 -0400
• Organization: @Home Network
• References: <7r7jvo\$ck4@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```William,

Here is what I got:

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

sol = DSolve[eqns, {x[t], y[t]}, t][] // ExpandAll // Simplify

xx[t_] = x[t] /. sol // ComplexExpand // Simplify

1/(a^2 + b^2)^2*
(E^(a*t)*(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] +
(a^2 + b^2)*(b*C + a*C)*Sin[b*t])/E^(a*t)

and

yy[t_] = y[t] /. sol // ComplexExpand // Simplify

1/(a^2 + b^2)^2*
(E^(a*t)*(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^2 + b^2)*(a*C - b*C)*Sin[b*t])/E^(a*t)

The answers look a lot nicer in NormalForm, but still pretty nice.  Hope
this helps.

Kevin

William M. MacDonald <wm2 at umail.umd.edu> wrote in message
news:7r7jvo\$ck4 at smc.vnet.net...
>
> 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.)
>
> --
> William M. MacDonald
> Professor of Physics
> University of Maryland
>
> Internet: wm2 at umail.umd.edu
>

```

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