function [ ] = prob_2_25
% 
% Written by:
% -- 
% John L. Weatherwax                2005-05-07
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----

options = odeset('Events',@events,'RelTol',1d-5,'AbsTol',1d-10);

y0 = [ 0 1 ]; 
[ts,ys,te,ye,ie] = ode45( @f, [0, 20*pi], y0, options );

figure;
plot( ts, ys(:,1), '-og' ); hold on; grid on; 
plot( te, ye(:,1), 'ob' ); 
figure; plot( abs(diff( te )-pi), '-o' ); 


y0 = [ 0 0.1 ]; 
[ts,ys,te,ye,ie] = ode45( @f, [0, 20*pi], y0, options );
figure;
plot( ts, ys(:,1), '-og' ); hold on;  grid on; 
plot( te, ye(:,1), 'ob' ); 
figure; plot( abs(diff( te )-pi), '-o' ); 


y0 = [ 0 0.01 ]; 
[ts,ys,te,ye,ie] = ode45( @f, [0, 20*pi], y0, options );
figure;
plot( ts, ys(:,1), '-og' ); hold on;  grid on; 
plot( te, ye(:,1), 'ob' ); 
figure; plot( abs(diff( te )-pi), '-o' );

return;



function [dydt] = f(t,y)
%
% y is 2x1
%
dydt = [ 
         y(2);
         -sin(y(1))
       ];

return;



function [value,isterminal,direction] = events(t,y)

global g nu;

value = y(1);
isterminal = 0;
direction = 0;

return;