% Program 6.3 Animation program for pendulum using IVP solver
% Inputs: int = [a b] time interval,
%  initial values ic = [y(1,1) y(1,2)], h = step size
% Calls a one-step method such as trapstep.m
% Example usage: pend([0 10],[pi/2 0],.05)
function pend(int,ic,h)
n=round((int(2)-int(1))/h); % plot n points in total
y(1,:)=ic;                % enter initial conds in y
t(1)=int(1);
clf;                      % clear screen
set(gca,'xlim',[-1.2 1.2],'ylim',[-1.2 1.2], ...
  'xtick',[-1 0 1],'ytick',[-1 0 1], ...
  'drawmode','fast','Visible','on','NextPlot','add');
plot(0,0,'ks');           % pivot where rod attached
axis square               % make aspect ratio 1 - 1
bob = line('color','r','Marker','.','markersize',40,...
    'erase','xor','xdata',[],'ydata',[]);
rod = line('color','b','LineStyle','-','LineWidth',3,...
    'erase','xor','xdata',[],'ydata',[]);
for k=1:n
  t(k+1)=t(k)+h;
  y(k+1,:)=trapstep(t(k),y(k,:),h);
  xbob = cos(y(k+1,1)-pi/2); ybob = sin(y(k+1,1)-pi/2);
  xrod = [0 xbob]; yrod = [0 ybob];
  set(rod,'xdata',xrod,'ydata',yrod)
  set(bob,'xdata',xbob,'ydata',ybob)
  drawnow; pause(h)
end

function y = trapstep(t,x,h)
%one step of the Trapezoid Method
z1=ydot(t,x);
g=x+h*z1;
z2=ydot(t+h,g);
y=x+h*(z1+z2)/2;

function z=ydot(t,y)
g=9.81;length=1;
z(1) = y(2);
z(2) = -(g/length)*sin(y(1));