function [t_k,N,Phi,Q] = weathervane_system(omega_n,zeta,q_C,dt,T)
%
% Inputs: 
%
% Written by:
% -- 
% John L. Weatherwax                2005-08-14
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----

a = -omega_n^2; 
b = -2*zeta*omega_n; 

% Generate the grid we consider measurements on:
N = T/dt;
t_k = 0:dt:T;

% Compute the discrete system matrix Phi:
F = [ 0, 1; -omega_n^2, -2*zeta*omega_n ];
Phi = expm( F * dt );

% Use the previous code to compute the discretized noise covariance matrix Q(\Delta t):
L = [ 0; 1 ];
L_Qc_LT = L * q_C * L';

Nsteps = 100; % number of integration steps 

Q = example_4_2_2_compute_qkm1( a, b, L_Qc_LT, dt, Nsteps ); % before multiplication of omega_n^4
Q = omega_n^4 * Q; % after multiplication of omega_n we have the complete process noise covariance