s1=figf_5(s,A)

function s1=figf_5(s,A)                                          
% Root locus vs. A for infinite-dimensional LQR for stabilizing
% tip angle using center torque of a uniform beam; a = lambda.
% T(s)=[ch(a)+c(a)]/[a^2(sh(a)c(a)-ch(a)s(a)]; a = sqrt(js)
% where s is in units of wo, wo^2=EI/sigma*L^4, Q in EI/L; 8/20/91
%
j=sqrt(-1); a=sqrt(j*s); n=cosh(a)+cos(a);
d=a^2*(sinh(a)*cos(a)-cosh(a)*sin(a)); y=A*n^2+j*d^2;
yp=2*A*n*(sinh(a)-sin(a))+4*j*d*((d/a)-a^2*sinh(a)*sin(a));
a=a-y/yp; s1=-j*a^2;