Re: Mathematica can't win against Tiger Woods

*To*: mathgroup at smc.vnet.net*Subject*: [mg19692] Re: Mathematica can't win against Tiger Woods*From*: weber at math.uni-bonn.de (Matthias Weber)*Date*: Sat, 11 Sep 1999 16:36:01 -0400*Organization*: RHRZ - University of Bonn (Germany)*References*: <7r7jvo$ck4@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

In article <7r7jvo$ck4 at smc.vnet.net>, "William M. MacDonald" <wm2 at umail.umd.edu> 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 > 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.) > {(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] - (b*C[3] + a*C[4])*Sin[b*t]))/E^(a*t))/ (a^2 + b^2)^2, (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*C[3] - b*C[4])*Sin[b*t]))/E^(a*t))/(a^2 + b^2)^2 } with Mathematica 3.0, using just DSolve[{x''[t]== - (a x'[t]+b y'[t]), y''[t]== - g - (a y'[t]- b x'[t])},{x,y},t]; {x[t],y[t]}/.%[[1]]; Simplify[%]; FullSimplify[%] Takes about 2 minutes in total. On a Mac. No fancy tricks. Of course there are always examples where system X will be better than system Y. The real trouble is caused not by the better features of system Y, but by the bugs of system X. Best, Matthias