function ydot = sect_5_4_ode_fn(t,y)
% SECT_5_4_ODE_FN - returns the time derivative needed to integrate the covariance evolution equations 
%
% Written by:
% -- 
% John L. Weatherwax                2005-08-14
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----

% some parameters:
omega_n = 10;
zeta = 0.3;
q = 10;

% extract the components:
y = y(:); 
s11 = y(1);
s12 = y(2);
s22 = y(3);

s11Squared   = s11^2;
s12Squared   = s12^2;
s22Squared   = s22^2;
omegaSquared = omega_n^2;

ydot = zeros(3,1);

ydot(1) = (s11*((10*s12Squared)/(s11Squared*s22Squared) + (2*s12*omegaSquared)/s22))/2. + ...
          s12*((-10*s12)/(s11*s22Squared) - (s11*omegaSquared)/s22 + (s12Squared*omegaSquared)/(s11*s22) + ...
          s22*(1/s11 + (2*s12*omega_n*zeta)/(s11*s22)));
        
ydot(2) = s11*((-10*s12)/(s11*s22Squared) - (s11*omegaSquared)/s22 + (s12Squared*omegaSquared)/(s11*s22) + ...
          s22*(1/s11 + (2*s12*omega_n*zeta)/(s11*s22))) + (s12* (10/s22Squared - (s12*omegaSquared)/s22 - 2*omega_n*zeta + (-(s12*omegaSquared) - 2*s22*omega_n*zeta)/s22))/2.;
      
ydot(3) = (s22*(10/s22Squared - (s12*omegaSquared)/s22 - 2*omega_n*zeta + (-(s12*omegaSquared) - 2*s22*omega_n*zeta)/s22))/2.;