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MathGroup Archive 1999

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Re: Mathematica can win against Tiger Woods

  • To: mathgroup at smc.vnet.net
  • Subject: [mg19705] Re: [mg19677] Mathematica can win against Tiger Woods
  • From: "Richard Finley" <rfinley at medicine.umsmed.edu>
  • Date: Sat, 11 Sep 1999 16:36:08 -0400
  • Sender: owner-wri-mathgroup at wolfram.com

William,
There are certainly strong and weak points for all the packages.  I think 
it depends to a large extent on your experience with the software you are 
working with and  the sophistication of the problems you are working on.  
A package like Mathematica is very sophisticated and handles a lot of problems in 
more generality than people sometimes want (just note all the messages 
asking for help about why Sqrt[x^2] doesn't simplify to x etc...) ...so 
you lose some ease of use for a more powerful (general) system.  But how 
you set up the problem also has a lot to do with it.....for example, the 
problem you describe is much more easily done in Mathematica if you solve it for 
four first order equations rather than two second order.  This is probably 
better pedagogically also as that is probably how you would solve it "by 
hand".  I solved the first two equations (for the velocities) and then 
substituted these solutions into the two equations for x[t] and y[t].  The 
first solution took 0.27 sec on a Pentium 450 Win98 and the second 1.43 
sec and the answer was essentially the same I got from "another" comparable
 software package with no need to simplify in either case (real expressions
 with no complex exponentials etc...).  To be honest, for particular 
problems like this I sometimes use one or another of the other packages, 
but I always come back to Mathematica in the end.  For teaching you can always 
write notebooks for students to handle all the messy details. 
regards,  RF

>>> "William M. MacDonald" <wm2 at umail.umd.edu> 09/09/99 12:19AM >>>

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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