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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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