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.