%% Models the simple pendulum using Euler's method. 
%% Usage: [t,th,w] = EulerPendulum([ic1,ic2],tmin,tmax,N)
%% Input:  ic1 and ic2  - the intial values of theta (th) and w (which is th').
%%         tmin - initial time
%%         tmax - final time
%%         N - number of steps
%% Output: t - Nx1 vector of time values
%%         th - Nx1 vector of angle values
%%         w - Nx1 vector of angular velocity values
function [t,th,w] = EulerPendulum(ic,tmin,tmax,N)
g = 9.81; L=1; % gravity and rod length

t = linspace(tmin,tmax,N)';
h = t(2) - t(1); % step size

th = zeros(size(t)); w = th; 
th(1)=ic(1); w(1)=ic(2); % initial conditions

for j=1:N-1
   th(j+1) = th(j)+h*w(j);
   w(j+1) = w(j) + h*(-g/L*sin(th(j)));
end

end