MathGroup Archive 2011

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: Integation Anomoly

  • To: mathgroup at smc.vnet.net
  • Subject: [mg117944] Re: Integation Anomoly
  • From: blamm64 <blamm64 at charter.net>
  • Date: Tue, 5 Apr 2011 06:43:34 -0400 (EDT)
  • References: <inc6kd$to$1@smc.vnet.net>

Sorry, I forgot to include the definitions of wCarStepR and wCarStepL
(thanks to Daniel).  With those definitions included in the proper
place, all the code should be as follows (you don't really need the
definition of wCarStepL to see the behavior I'm seeing, but I left it
in there).  The 'final' definition of wCarStep would be a piecewise
using 0 for t < 0, wCarStepR[t] from 0 <= t <= twTr, and wCarStepL[t]
from t > twTr.


row:=Sqrt[dwCar^2+1]*twTr/dwCar;
tow:=twTr+twTr/(dwCar^2)-row/dwCar;
wCarStepR[t_]=row-Sqrt[row^2-t^2];
wCarStepL[t_]=dwCar*(t-tow);
Assuming[twTr>0 && dwCar>0,(wCarStepR[twTr]==wCarStepL[twTr])//
FullSimplify]
thCA1s[t_]=Assuming[0<=t<=twTr && twTr>0 &&
dwCar>0,Integrate[wCarStepR[tau],{tau,0,t}]]
thCA2s[t_]=Assuming[0<t<=twTr && twTr>0 &&
dwCar>0,Integrate[wCarStepR[tau],{tau,0,t}]]
thCA1s[t]==thCA2s[t]
thCA1sd[t_]:=Assuming[0<=t<=twTr && twTr>0 &&
dwCar>0,Integrate[wCarStepR[tau],{tau,0,t}]]
thCA2sd[t_]:=Assuming[0<t<=twTr && twTr>0 &&
dwCar>0,Integrate[wCarStepR[tau],{tau,0,t}]]
thCA1sd[t]==thCA2sd[t]
Number Trials
dwCar=16;twTr=1/500;N[{row,tow},10]
thCA1s[t]
thCA1sd[t]
(thCA1s[t]==thCA1sd[t])//FullSimplify
(thCA2s[t]==thCA2sd[t])//FullSimplify
{thCA1sd[t]==thCA2sd[t],thCA1s[t]==thCA2s[t]}
Clear[dwCar,twTr]
dwCar=15;twTr=1/500;N[{row,tow},10]
thCA1s[t]
thCA1sd[t]
(thCA1s[t]==thCA1sd[t])//FullSimplify
(thCA2s[t]==thCA2sd[t])//FullSimplify
{thCA1sd[t]==thCA2sd[t],thCA1s[t]==thCA2s[t]}
(thCA1sd[t]==thCA2sd[t])//FullSimplify
a=thCA1sd[t]//FullSimplify;b=thCA2sd[t]//FullSimplify;a==b

-Brian L.


  • Prev by Date: Re: PlotLegend and Show
  • Next by Date: Re: Integrate gives wrong results for a simple polynomial
  • Previous by thread: Integation Anomoly
  • Next by thread: Take the Wolfram Demonstrations Challenge and win great prizes!