1-2*cos(al​pha1)+2*co​s(alpha2)-​2*cos(alph​a3); 1-2*cos(5*​alpha1)+2*​cos(5*alph​a2)-2*cos(​5*alpha3) how to solve this nonlinear equation using matlab?by using newton raphson method or fsolve..please help me...

nonlinear equation solve

[Torsten]

What equation ? I only see a mathematical expression.

And what is the variable you want to solve for ?

Best wishes

Torsten.

Answer 1

[Walter Roberson]

Assuming the system

[1-2*cos(alpha1)+2*cos(alpha2)-2*cos(alpha3), 1-2*cos(5*alpha1)+2*cos(5*alpha2)-2*cos(5*alpha3)]

The system has two trivial roots: alpha1 = pi/3 for all alpha2 and alpha3; and alpha3 = pi/3 for all alpha1 and alpha2. It also has the simple root alpha2 = 2*pi/3 and alpha3 = pi - alpha1 for all alpha1.

There is an additional pair of roots that would take some meaningful searching for and is worth doing an exercise for, but with those other three roots being so simple it is hardly worth bothering.

If you want to try with fsolve then:

fun = @(alpha1, alpha2, alpha3) [1-2*cos(alpha1)+2*cos(alpha2)-2*cos(alpha3), 1-2*cos(5*alpha1)+2*cos(5*alpha2)-2*cos(5*alpha3)];
f3 = @(alpha) fun(alpha(1), alpha(2), alpha(3));

fsolve(f3, rand(1,3))