function ydot = sect_5_4_ode_fn_part_a(t,y)
% SECT_5_4_ODE_FN_PART_A - 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.
% 
%-----

% the common terms for all parts (ignores the measurement term -S S^T H^T R_C^{-1} H S):
ydot = sect_5_4_ode_fn(t,y);

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

s22Squared = s22^2;

% add in the measurement term (-S S^T H^T R_C^{-1} H S):
%
ydot(1) = ydot(1);
ydot(2) = ydot(2) - s12*s22Squared;
ydot(3) = ydot(3) - 0.5*(s12^3);