function [J] = sect_4_prob_2_J_min_fn(lambda_0, t_0,t_f,x_0_ic, u0,x0,n,a,b,c)
%   
% Written by:
% -- 
% John L. Weatherwax                2006-08-28
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----

% First integate the given differential equations from t=0 to t=t_f: 
% 
sol = ode23s( @(t,x) sect_4_prob_2_J_ode_fn(t,x, u0,x0,n,a,b,c), [t_0,t_f], [lambda_0;x_0_ic] );

lambda_t = sol.y(1,:); % extract lambda(t) 

% Second evaluate the expression for J: 
% 
J = 0.5 * ( lambda_t(end)^2 );