function [] = prob_3_22(T)
% 
% Written by:
% -- 
% John L. Weatherwax                2005-04-13
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----

guess = [ 1; 0; ];
solinit = bvpinit(linspace(0,T,10),guess);
sol = bvp4c(@f,@bcs,solinit);

figure; plot( sol.x, sol.y(1,:), '-bo' ); hold on; grid on;
tmp=deval(sol,0);
fprintf( 'Theta Prime at 0 = %f\n', tmp(2) );

function [res] = bcs(ya,yb)
% BCS - 
%
res = [ ya(1);
        yb(1)-pi;
       ];

function [ ode ] = f(x,y)
% F - 
% y(1)=theta(x);y(2)=theta'(x);
 
ode = [  
    y(2);
    -sin(y(1));
      ];