%%% equ.m: this script defines the system of ODE's that describes the 
%%% motion ofa pendulum with friction = eps * velocity. 
%%% requires the driver file phase.m
%
% The ODE is u''(t) - eps*u'(t) + u = 0
%
% We can rewrite this second-order ODE as two first-order equations
% by introducing v(t)=u'(t). Matlab needs this system of ODEs written 
% in the form of a matrix times a vector, so we rewrite the system as
%        /        \ /      \       /      \
%        | 0  1   | | y(1) |       | y(1)'|
%        |        | |      |  ---  |      |
%        |-1  eps | | y(2) |  ---  | y(2)'|
%        \        / \      /       \      /
%
% where y(1) = u and y(2) = v and yp is the vector containing y(1)'
% and y(2)'.
%
% We define this system as the fuction equ(t,y), which is called in
% phase.m

function yp = equ(t,y)
	eps = 1.0e-1;
	yp = [0.0 1.0; -1.0 eps]*y;