MATLAB: I am getting empty sym for vpasolve

MATLABplotvpasolve

Hi all,
this is my code
syms theta1 theta2 gama M l
eqn = theta1 == 2*atan((2*tan(theta2/2)*tan(gama/2 - theta2/2) + (4*tan(theta2/2)^2 - 4*M^2*tan(theta2/2)^2 - 4*M^2*tan(gama/2 - theta2/2)^2 - M^2*gama^2*l^2 - 8*M^2*tan(theta2/2)*tan(gama/2 - theta2/2) - 4*M^2*gama*l*tan(theta2/2) - 4*M^2*gama*l*tan(gama/2 - theta2/2) - M^2*gama^2*l^2*tan(theta2/2)^2*tan(gama/2 - theta2/2)^2 + 2*M^2*gama^2*l^2*tan(theta2/2)*tan(gama/2 - theta2/2) + 4*M^2*gama*l*tan(theta2/2)*tan(gama/2 - theta2/2)^2 + 4*M^2*gama*l*tan(theta2/2)^2*tan(gama/2 - theta2/2) + 4)^(1/2) - 2)/(2*tan(theta2/2) + 2*M*tan(gama/2 - theta2/2) + 2*M*tan(theta2/2) + M*gama*l - M*gama*l*tan(theta2/2)*tan(gama/2 - theta2/2)) - (2*tan(theta2/2)*tan(gama/2 - theta2/2))/(2*tan(theta2/2) + 2*M*tan(gama/2 - theta2/2) + 2*M*tan(theta2/2) + M*gama*l - M*gama*l*tan(theta2/2)*tan(gama/2 - theta2/2)));
F=1.06;
gama=pi/F;
thetac=0:0.2:gama;
theta2=thetac;
l=0.2181818;
M=0.960615;
seqn = subs(eqn);
sol = vpasolve(seqn)
alpha_1=theta1/thetac;
plot(thetac,alpha_1)
When I am trying to find solutions for theta1, it is giving me empty sym.
Can anyone help me regarding this?

Best Answer

Since thetac is an array of 15 elements, you are trying to solve a system of 15 incompatible equations, therefore, there is no answer. You should solve the equation for each value of thetac.
syms theta1 theta2 gama M l
eqn = theta1 == 2*atan((2*tan(theta2/2)*tan(gama/2 - theta2/2) + (4*tan(theta2/2)^2 - 4*M^2*tan(theta2/2)^2 - 4*M^2*tan(gama/2 - theta2/2)^2 - M^2*gama^2*l^2 - 8*M^2*tan(theta2/2)*tan(gama/2 - theta2/2) - 4*M^2*gama*l*tan(theta2/2) - 4*M^2*gama*l*tan(gama/2 - theta2/2) - M^2*gama^2*l^2*tan(theta2/2)^2*tan(gama/2 - theta2/2)^2 + 2*M^2*gama^2*l^2*tan(theta2/2)*tan(gama/2 - theta2/2) + 4*M^2*gama*l*tan(theta2/2)*tan(gama/2 - theta2/2)^2 + 4*M^2*gama*l*tan(theta2/2)^2*tan(gama/2 - theta2/2) + 4)^(1/2) - 2)/(2*tan(theta2/2) + 2*M*tan(gama/2 - theta2/2) + 2*M*tan(theta2/2) + M*gama*l - M*gama*l*tan(theta2/2)*tan(gama/2 - theta2/2)) - (2*tan(theta2/2)*tan(gama/2 - theta2/2))/(2*tan(theta2/2) + 2*M*tan(gama/2 - theta2/2) + 2*M*tan(theta2/2) + M*gama*l - M*gama*l*tan(theta2/2)*tan(gama/2 - theta2/2)));
F=1.06;
gama=pi/F;
thetac=0:0.2:gama;  
l=0.2181818;
M=0.960615;  
for k=1:numel(thetac)
    theta2=thetac(k);
    seqn = subs(eqn);
    sol(k) = vpasolve(seqn)
end
alpha_1=sol./thetac;
plot(thetac,alpha_1)
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