Solve these nonlinear equations for the uknowns, the angle \"phi\" and \"s\" usi

ID: 2994596 • Letter: S

Question

Solve these nonlinear equations for the uknowns, the angle "phi" and "s" using the newton-raphson method.

I know this is how the m file is supposed to look, but I'm not sure how to implement using the above equations to solve for phi and s.

function [root,ea,iter] = newtraph(y,dy,x,et)

max_it=1000;

iter = 0;

% Modified secant iteration

while(1)

xold = x; % store previous guess 'xr' in 'xrold' to estimate error

% derivative estimation by fraction perturbation

x = xold - y(x)/dy(x); % Modified secant formula

iter = iter + 1; % update iteration index

if x ~=0

ea = abs((x-xold)/x)*100;

end % estimate approx relative error

if ea <= et

break

end;

if iter >= max_it

error('max iteration reached')

end; % check for convergence; if so, stop

end

root = x; % root value is set to the final value of the guess, once it is conveged

we have

R sin (theta ) + L sin(phi) = H ....(1)

R cos(theta) + L cos(phi) =s....(2)

Multuply cos (theta ) to 1st eqn and sin(theta) to 2nd eqn and subtract .

We get

L( sin(phi)cos(theta) - cos(phi) sin(theta) ) = H cos(theta) - s sin(theta)

L sin( phi -theta ) =H cos(theta) - s sin(theta)

phi = arcsin ([H cos(theta) - s sin(theta)] /L) + theta (Theta is known value)

So basically now we have expressed phi interms of s

Now s =R cos(theta) + L cos(phi) ( from eqn 2)

So we have expressed phi in terms of phi.

Now simply call the above function you have built using this equation of phi and solve it to find the roots ..!!!