r=0.18;
lambda=0.9;
a0=0.4;
a1=0.15;
kc=1.37*10^3;
b=0.089;
kpsi=8.14*10^5;
s_LB=0.4;
beta_LB=5;
psi=37;
W=30;
c=0.8;
syms thetaF thetaR thetaM sigmaLB jx KXsym tx Fz h theta
eqn1= thetaF==double(acosd(1-h/r));
eqn2= thetaR==double(acosd(1-lambda*h/r));
eqn3= thetaM==double((a0+a1)*thetaF);
eqn4= sigmaLB==double(r*((kc/b)+kpsi)*(cosd(theta)-cosd(thetaF)));
eqn5= jx==double(r*(thetaF-theta-(1-s_LB)*(sind(thetaF)-sind(theta))));
eqn6= KXsym==double(0.043*beta_LB+0.036);
eqn7= tx==double((c+sigmaLB*tand(psi))*(1-exp(-jx/KXsym)));
eqn8= Fz==integral(@(theta)r*b*(tx*sind(theta)+sigmaLB*cosd(theta)),thetaR,thetaF);
eqn9= W==Fz;
[thetaSol,hSol]=vpasolve([eqn1 eqn2 eqn3 eqn4 eqn5 eqn6 eqn7 eqn8 eqn9],[theta,h]);
I hope you are all doing well despite the virus. My goal is to obtain the values of theta and h for Fz=W.
r, lambda, a0, a1, kc, b, kpsi, s_LB, beta_LB, psi, c and W are known constants. Because of MATLAB giving me the error "A and B must be floating-point scalars" in eqn8, I added the double(). Now I have the error Unable to convert "expression into double array". I made some research and I think it doesn't work because it is in a loop but I didn't clearly understand. That's why I am now asking for your help.
First I would like to know if MATLAB can resolve this system numerically? If yes, I would like to know where I made my error(s) to correct it (them). I'll add that I am using 2019b.
Thank you in advance for your help.
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