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# How do I solve this equation correctly?

Posted 11 years ago
 HelloI did a force calculation in the attached mathematica code. Everything is working good as far as i see, until my last equation, solving for the forces. I'm under time pressure, and am very happy about any help which can solve this problem.The error I get is the equation "is not a quantified system of equations and inequalities"Thank you very much for your time  ClearAll;    (*wbeta[t] =   wepsilon[t] =   b = 0.09  a = 0.04  mM = 1.500  RM = 0.02  LM = 0.22 mK = 1.500 RK = 0.03 LK = 0.12*)   "Kräfte"  KraftO = { FOx[t ], FOy[t] , FOz[t] }; KraftB = { FBx[t] , FBy[t] , FBz[t] };  (* Gewichtskraft im K System : *)  KraftG = {  0, 0 , -(mM + mK)*9.81 };  MatrixForm[KraftO] MatrixForm[KraftB] MatrixForm[KraftG]   "Winkel"   alpha = 45 \[Degree] beta = wbeta[t] gamma = 55 \[Degree] epsilon = wepsilon[t] delta = 25 \[Degree]  "Winkel-Geschwindigkeiten"  valpha = { 0 , 0, 0 } vbeta = { 0, 0, D[beta, t] } vgamma = { 0, 0, 0} vepsilon = { 0, 0, D[epsilon, t]}  "Winkel-Beschleunigungen"  aalpha = { 0, 0, 0} abeta = { 0, 0, D[D[beta, t]]} agamma = { 0, 0, 0} aepsilon = { 0, 0, D[D[epsilon, t]] }  "1. Rotation um y (math negativ)"  AAI = {{ Cos[alpha] , 0 , Sin[alpha] } , {0, 1, 0}, {-Sin[alpha], 0,      Cos[alpha]}};  MatrixForm[AAI]  "2. Erstes Gelenk: Rotation um z (math negativ)"  ABA = {{ Cos[beta] , Sin[beta] , 0 } , {-Sin[beta] , Cos[beta] ,      0}, {0 , 0 , 1 }};  MatrixForm[ABA]  "3. Winkel im Stab: Rotation um y (math positiv)"  ACB = {{Cos[gamma] , 0 , -Sin[gamma] }, { 0, 1 , 0 }, { Sin[gamma],      0 , Cos[gamma] }};  MatrixForm[ACB]  "4. Zweites Gelenk: Rotation um z (math positiv)"  AKC = {{ Cos[epsilon] , Sin[epsilon] , 0 }, { -Sin[epsilon] ,      Cos[epsilon] , 0 }, { 0 , 0 , 1 }};  MatrixForm[AKC]  "5. Drehung von K System zum Kopf um y ( math positiv)"  AEK = {{ Cos[delta] , 0 , -Sin[delta]}, {0, 1, 0}, {Sin[delta] , 0 ,      Cos[delta]}};  MatrixForm[AEK]  "Ortsvektoren"  ra =  { x_s , 0 , z_s }; rb = {b, 0, 0}; rc = {a, 0, 0}  ;  MatrixForm[ra] MatrixForm[rb] MatrixForm[rc]   "Resultierender Ortsvektor bestimmen"  rOS = ra + (AKC . rb) + (AKC . ACB . rc);rOB =  ra + (AKC . rb);MatrixForm[rOS]"abgeleiteter Ortsvektor"rOSabl = D[rOS, t];MatrixForm[rOSabl]"Winkelgeschwindigkeit von S im K-System"omegaS = vepsilon + AKC . vgamma + AKC . ACB . vbeta +    AKC . ACB . ABA . valpha;MatrixForm[omegaS]"Geschwindigkeiten von S im K-System"vS = rOSabl + omegaS \[Cross] rOS;MatrixForm[vS]"abgeleiteter Geschwindigkeitsvektor "vOSabl = D[vS, t];MatrixForm[vOSabl]"Beschleunigung von S im K-System"aS = vOSabl + omegaS  \[Cross] vS;MatrixForm[aS]"Winkelbeschleunigung von S im K-System"PsiS = D[omegaS, t];MatrixForm[PsiS]"Trägheitstensor Motor"ThetaM = {{(3/20) mM  RM^2 + (3/80) mM LM^2, 0,     0}, {0, (3/20) mM RM^2 + (3/80) mM LM^2  , 0} , { 0,     0, (3/10) mM RM^2 }};MatrixForm[ThetaM]"Trägheitstensor Kopf"ThetaK = {{(3/20) mK  RK^2 + (3/80) mK LK^2, 0,     0}, {0, (3/20) mK RK^2 + (3/80) mK LK^2  , 0} , { 0,     0, (3/10) mK RK^2 }};MatrixForm[ThetaK]"Transformation vom Kopf ins K-System"ThetaKK = AEK . ThetaK . Transpose[AEK];MatrixForm[ThetaKK]"Totales Trägheitsmoment"ThetaTot = ThetaM + ThetaKK ;MatrixForm[ThetaTot]"Momentengleichgewicht im Ursprung"MO = rOB  \[Cross] KraftB + rOS \[Cross] KraftG;MatrixForm[MO]"Impulssatz bezüglich Schwerpunkt"p = (mM + mK) * vS;MatrixForm[p]"Drallsatz bezügliche Schwerpunkt"(* Drall muss immer bezüglich eines festen Punktes gemacht werden, \dieser ist O *)LO = rOS \[Cross] p + ThetaTot . omegaS;MatrixForm[LO]"Ableitung des Impulssatzes"pabl =  D[p, t] + omegaS \[Cross] p;MatrixForm[pabl]"Ableitung des Drallsatzes"LOabl = D[pabl, t] + omegaS \[Cross] LO;MatrixForm[LOabl]"Nach Kräften im Punkt B auflösen/ Solving for forces, everything works fine until here, the error occures" (* Idee funktioniert*) Solve[ {LOabl[[1]] == MO[[1]] , LOabl[[2]] == MO[[2]] ,     LOabl[[3]] == MO[[3]] } {FBx[t] , FBy[t] , FBz[t]}];"Kräfte im Punkt 0 im A - System"FOA = - AKC . ACB . ABA . (-KraftB);MatrixForm[FOA]
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Posted 11 years ago
 Thank you very much!I get the problem now, that my forces are not displayed in the output, can anyone help?Thanks, i appreciate a lot!
Posted 11 years ago
 Missing comma between the two lists being given to Solve.You might also be able to replace the first list with just LOabl==MO.