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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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