Re: Mathematica can't win against Tiger Woods

• To: mathgroup at smc.vnet.net
• Subject: [mg19687] Re: Mathematica can't win against Tiger Woods
• From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
• Date: Sat, 11 Sep 1999 16:35:58 -0400
• Organization: Universitaet Leipzig
• References: <7r7jvo\$ck4@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Hi William,

first of all the result is not very complicated. It is less than 10
printed pages and it has no special function like a hypergeometric one
in it.

Typical a computer algebra uses the most general result or the most
general algorithm. It must do so to fit into all possible cases.
g is real and positive.

For your problem it seems to be better to calculate the velocities x'[t]
and y'[t]
and get
{{vx[t] -> (b*g)/(a^2 + b^2) +
(C[1]*Cos[b*t] - C[2]*Sin[b*t])/E^(a*t),
vy[t] -> -((a*g)/(a^2 + b^2)) +
(C[2]*Cos[b*t] + C[1]*Sin[b*t])/E^(a*t)}}

a very simple one. It is the second integration (to obtain x[t] and
y[t])
that causes Mathematica to split Sin[] and Cos[] int exponentials and it
must do so due to the Exp[-a*t] term.
If you integrate the vx[t] and vy[t] to obtain the positions and run
FullSimplify[] again you get

{(E^(a*t1)*(b*g*t1 + a*C[1] - b*C[2]) +
(-(a*C[1]) + b*C[2])*Cos[b*t1] + (b*C[1] + a*C[2])*
Sin[b*t1])/((a^2 + b^2)*E^(a*t1)),
(E^(a*t1)*(-(a*g*t1) + b*C[1] + a*C[2]) -
(b*C[1] + a*C[2])*Cos[b*t1] + (-(a*C[1]) + b*C[2])*
Sin[b*t1])/((a^2 + b^2)*E^(a*t1))}

and the answer can't be more more simple.

Hope that helps
Jens

"William M. MacDonald" wrote:
>
> 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
>  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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