Re: Mathematica can't win against Tiger Woods
- To: mathgroup at smc.vnet.net
- Subject: [mg19686] Re: Mathematica can't win against Tiger Woods
- From: "Kevin J. McCann" <kevinmccann at Home.com>
- Date: Sat, 11 Sep 1999 16:35:58 -0400
- Organization: @Home Network
- References: <7r7jvo$ck4@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
William,
Here is what I got:
eqns = {x''[t] == - (a x'[t] + b y'[t]), y''[t] == - g - (a y'[t] - b
x'[t])}
sol = DSolve[eqns, {x[t], y[t]}, t][[1]] // ExpandAll // Simplify
<<< Long Ugly Answer >>>
xx[t_] = x[t] /. sol // ComplexExpand // Simplify
1/(a^2 + b^2)^2*
(E^(a*t)*(a^4*C[1] + a^3*C[3] + a*b*(-2*g + b*C[3]) +
b^3*(g*t + b*C[1] - C[4]) +
a^2*b*(g*t + 2*b*C[1] - C[4])) -
(a^2 + b^2)*(a*C[3] - b*C[4])*Cos[b*t] +
(a^2 + b^2)*(b*C[3] + a*C[4])*Sin[b*t])/E^(a*t)
and
yy[t_] = y[t] /. sol // ComplexExpand // Simplify
1/(a^2 + b^2)^2*
(E^(a*t)*(a^4*C[2] + b^2*(-g + b*(b*C[2] + C[3])) +
a^2*(g + b*(2*b*C[2] + C[3])) +
a^3*(-g*t + C[4]) + a*b^2*(-g*t + C[4])) -
(a^2 + b^2)*(b*C[3] + a*C[4])*Cos[b*t] -
(a^2 + b^2)*(a*C[3] - b*C[4])*Sin[b*t])/E^(a*t)
The answers look a lot nicer in NormalForm, but still pretty nice. Hope
this helps.
Kevin
William M. MacDonald <wm2 at umail.umd.edu> wrote in message
news:7r7jvo$ck4 at smc.vnet.net...
>
> 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
>