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MathGroup Archive 1999

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Re: Mathematica can't win against Tiger Woods

  • To: mathgroup at smc.vnet.net
  • Subject: [mg19693] Re: [mg19677] Mathematica can't win against Tiger Woods
  • From: "Andrzej Kozlowski" <andrzej at tuins.ac.jp>
  • Date: Sat, 11 Sep 1999 16:36:01 -0400
  • Sender: owner-wri-mathgroup at wolfram.com

I don't think of myself as a "computer algebra nerd" and I don't play golf 
but it seems to me that Mathemaitca does this problem rather well:

In[2]:=
solution = {y[t], x[t]} /. DSolve[{x''[t] == - (a x'[t] + b y'[t]),
     y''[t] == - g - (a y'[t] - b x'[t])}, {y[t], x[t]}, t];

In[3]:=
Simplify[ComplexExpand[solution, TargetFunctions -> {Im, Re}]]

Out[3]=
      1        a t   4         3
{{---------- (E    (a  C[1] + a  (-g t + C[3]) +
    2    2 2
  (a  + b )

             2                  2
          a b  (-g t + C[3]) + b  (-g + b (b C[1] + C[4])) +

           2
          a  (g + b (2 b C[1] + C[4]))) -

         2    2
       (a  + b ) (a C[3] + b C[4]) Cos[b t] -

         2    2                                  a t
       (a  + b ) (-b C[3] + a C[4]) Sin[b t]) / E   ,

       1        a t   4         3
   ---------- (E    (a  C[2] + b  (g t + b C[2] - C[3]) +
     2    2 2
   (a  + b )

           2                              3
          a  b (g t + 2 b C[2] - C[3]) + a  C[4] +

          a b (-2 g + b C[4])) -

         2    2
       (a  + b ) (-b C[3] + a C[4]) Cos[b t] +

         2    2                                 a t
       (a  + b ) (a C[3] + b C[4]) Sin[b t]) / E   }}


--
Andrzej Kozlowski
Toyama International University
JAPAN
http://sigma.tuins.ac.jp
http://eri2.tuins.ac.jp


----------
>From: "William M. MacDonald" <wm2 at umail.umd.edu>
To: mathgroup at smc.vnet.net
>To: mathgroup at smc.vnet.net
>Subject: [mg19693] [mg19677] Mathematica can't win against Tiger Woods
>Date: Thu, Sep 9, 1999, 3:19 PM
>

>
> 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
>  linearly  proportional to velocity, instead of the actual quadratic
>  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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