clear all
clc
f=@(t,x)([320*pi*cos(x(2)+8*pi*t)/(178*sin(x(2)-x(1)));
320*pi*cos(x(1)-8*pi*t)/(76*sin(x(1)-x(2)))]);
[t X]=ode45(f,[0 pi/20],[1/2/pi 52/2/pi]);
dx1=320*pi*cos(X(:,2)+8*pi*t)./(178*sin(X(:,2)-X(:,1)));
dx3=320*pi*cos(X(:,1)-8*pi*t)./(76*sin(X(:,1)-X(:,2)));
d2x1=diff(dx1)./diff(t);
d2x3=diff(dx3)./diff(t);
figure(1)
plot(t,X(:,1),t,X(:,2)),legend('x1','x3')
figure(2)
plot(t,dx1,t,dx3),legend('dx1/dt','dx3/dt')
figure(3)
plot(t(1:length(t)-1),d2x1,t(1:length(t)-1),d2x3),legend('d^{2}x1/dt^{2}','d^{2}x3/dt^{2}')