Solving a matrix equation with a parameter in the coefficient matrix

Hello,

I'm asked to give an expression of S and F in function of theta. This is possible due to 3 given equations. If I make a matrix of these equations and use the linsolve there is an error because of the parameter thetea. Can someone help?

Kind regards,

Tuur

syms theta S F
r = 0.025;
h = 0.3;
rho = 7850;
g = 9.81;


m = r^2 * pi * h * rho;
phi = atan((0.15 - 0.15*sin(theta))/(0.15*cos(theta)))

F_g = [0 , -m * g];
F_s = [-S*cos(phi), S*sin(phi)];
F_p = [F*cos(theta), F*sin(theta)];


eq1 = F_g(1) + F_s(1) + F_p(1) == 0;
eq2 = F_g(2) + F_s(2) + F_p(2) == 0;
eq3 =  0.15*cos(theta)*F*sin(phi) - 0.15*sin(theta)*F*cos(phi) + m * g * 0.15 * cos(theta) == 0;

A = [-cos(phi), cos(theta); sin(phi), sin(theta); 0, 0.15*cos(theta)*sin(phi) - 0.15*sin(theta)*cos(phi)]
B = [0; m * g ; -m * g * 0.15 * cos(theta)]

Answer 1

[Stephan]

syms theta S F
r = 0.025;
h = 0.3;
rho = 7850;
g = 9.81;

m = r^2 * pi * h * rho;
phi = atan((0.15 - 0.15*sin(theta))/(0.15*cos(theta)));

F_g = [0 , -m * g];
F_s = [-S*cos(phi), S*sin(phi)];
F_p = [F*cos(theta), F*sin(theta)];

eq(1) = F_g(1) + F_s(1) + F_p(1) == 0;
eq(2) = F_g(2) + F_s(2) + F_p(2) == 0;
eq(3) =  0.15*cos(theta)*F*sin(phi) - 0.15*sin(theta)*F*cos(phi) + m * g * 0.15 * cos(theta) == 0;

% New equations 
eqn(1) = lhs(eq(1)) == lhs(eq(3));
eqn(2) = lhs(eq(2)) == lhs(eq(3));

sol = solve(eqn,F,S)
pretty(sol.F)
pretty(sol.S)

[Tuur Vanderhaegen]

Thank you very much :)