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matlabnumerical-methodsnewtons-method

Newton's Method for System of Equations in MATLAB

I have tried to implement Newton's method for a system of equations, but I don't think it works correctly. I should get angles around [60 22.5 -60] degrees but right now I get [995 90 -230] degrees. Can someone see what's wrong with my code?

hold on

l = 2;
L1 = 1;
L2 = 1;
L3 = 1;
m1 = 1;
m2 = 1;

% The system of equations to solve
%l = L1cos(u1)+L2cos(u2)+L3cos(u3);
%0 = L1sin(u1)+L2sin(u2)+L3sin(u3);
%0 = m2tan(u1)-(m1+m2)tan(u2)+m1tan(u3);

u = [pi/3 pi/8 -pi/3]

for i = 1:10
    F = [L1*cos(u(1))+L2*cos(u(2))+L3*cos(u(3))-l, L1*sin(u(1))+L2*sin(u(2))+L3*sin(u(3)), m2*tan(u(1))-(m1+m2)*tan(u(2))+m1*tan(u(3))];
    DF = [-L1*sin(u(1)) -L2*sin(u(2)) -L3*sin(u(3)); L1*cos(u(1)) L2*cos(u(2)) L3*cos(u(3)); m2*sec(u(1))^2 -(m1+m2)*(sec(u(2))^2) m1*sec(u(3))^2];
    u1 = u' + inv(DF)*F';
    u = u1';
end

rad = u1;
deg = (180/pi)*u1;
Solution

  • Try replacing the following line 

    u1 = u' + inv(DF)*F';

    with

    u1 = u' - inv(DF)*F';

    When I make this change, the solution I get is [60,0,-60] which does correctly solve the three equations.