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MathGroup Archive 1999

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Mathematica can't win against Tiger Woods

  • To: mathgroup at smc.vnet.net
  • Subject: [mg19677] Mathematica can't win against Tiger Woods
  • From: "William M. MacDonald" <wm2 at umail.umd.edu>
  • Date: Thu, 9 Sep 1999 02:19:47 -0400
  • Sender: owner-wri-mathgroup at wolfram.com

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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