I want to calculate "a" in the following equation using the Newton- Raphson method:

\(

M = \phi _2*S*\phi _1

|eig( M)| - 0.8241 = 0

\)

With M, phi1 nad phi2 are matrices and S is given by:

\(

S = \left[ \begin{matrix} 1 & 0 \\

\frac{Vi}{x2-x1-aV\omega cos(\omega bT) - C} & 1 \end{matrix} \right]

\)

Besically all the variables are known apart from "a" thus using newton raphson we can find "a".

The way I have approached his is by taking the derivative of S wit hrespect to "a", thus

\(

S' = \left[ \begin{matrix} 1 & 0 \\

\frac{Vi*V\omega cos(\omega bT)}{(x2-x1-aV\omega cos(\omega bT) - C)^2} & 1 \end{matrix} \right]

\)

\(

M' = \phi _2*S'*\phi _1

|eig( M')| = 0

\)

In matlab, I enter all these equations and state that for Newton Raphson:

\(

a_{n+1} = a_n - \frac{y(a_n)}{y'(a_n)}

\)

\(

y(a_n) = |eig(M)| - 0.8241

\)

\(

y'(a_n) = \frac{eig(M')}{|eig(M')|}

\)

I then loop this a couple of times. Every loop generates a new "a" which is entered and the equations calculated again and again derived.

But you guessed, it is not working. Now, I was hoping someone could tell me if I had made errors towards the derivation during the various steps or not. Or maybe someone spots an other problem?