%   
% 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.
% 
%-----

close all; clc; clear; 

% set the constants of this problem: 
t_0     = 0.; 
t_f     = 10.; 
gamma_0 = pi/2.; 
gamma_d = pi/3.;
v_0     = 100.; 

d_gamma = 1; % test the two values of d_gamma 
%d_gamma = 10; % test the two values of d_gamma 

% find the optimal value for [alpha_0,alpha_1]: 
%  
alphas = fminsearch( @(x) sect_3_prob_2_part_d_J_min_fn(x(1), x(2), t_0, t_f, v_0, gamma_0, gamma_d, d_gamma), [ 0., 0. ] );
alphas

% evaluate J at this value of alpha
sect_3_prob_2_part_d_J_min_fn(alphas(1), alphas(2), t_0, t_f, v_0, gamma_0, gamma_d, d_gamma)

% look at how well the various end conditions match
sol = ode45( @(t,x) sect_3_prob_2_part_d_J_ode_fn(t,x, alphas(1),alphas(2)), [t_0,t_f], [v_0;gamma_0] );
gamma_d - sol.y(2,end)