Hello
I 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]