function xdot = nonlinear (t, x)
% 
% Nonlinear system simulation example 
% USE THIS FILE AS A TEMPLATE BY SUBSTITUTING YOUR OWN
% EQUATIONS ETC
%
% This is an example of an m-file function for the simulation
% of linear and non-linear dynamic systems represented as a
% system of first order dfqs
%
% this function may be called by ode23, ode45, rk45, etc.
%
% Inputs: 
% x    : vector of current states
% t    : time value
%
% Output:
% xdot : vector with results
%
% Define Local Parameters
% 
omsq  = 10.0 ;
alpha = 3.0 ;

%
% Establish the input
%
u = 0.0; 

% 
% Perform any algebraic calculations
%


%
% Describe the Nonlinear / Linear dynamics
% Example for a case where the dynamics change
% depending on the time ie 
% system parameters are time depended
%
if t > 1
   xdot(1) = x(2);
   xdot(2) = -10.0 * omsq * x(1) - 2.0 * alpha * x(2) + omsq*u;
else
   xdot(1) = x(2);
   xdot(2) = -omsq * x(1) - 20.0 * alpha * x(2) + omsq*u;
end   

xdot = xdot'; % transpose first order dfq equations

% end of m-file
===========================


% Solving this problem using Matlab and ode23 function

% MATLAB COMMAND WINDOW - MATLAB COMMAND WINDOW
% NOTE:
% you can get help about ode23 using 
>> help ode23

> x0 = [1 0];      % Define Initial Conditions
> simtime = [0 10]; % Define the simulation time 
> [t, y] = ode23('nonlinear', simtime, x0 ); % call ode23
> plot(t,y)         % Plot results