% M-file name: equations.m
% M-file type: Function file

% This function file obtains suspension forces and moments from function file
%'wheelset_suspension.m' and uses them to solve the single wheelset dynamic equations by
% invoking the function 'wheelset' .


% At the end of the simulation, MATLAB stores each degree of freedom as a column array and
% the entire solution as a matrix. The solution matrix in this program has been named 'x'. 
% Hence, in this case, the solution matrix 'x' will have 6 columns. The number of rows of 'x'
% will be equal to the total number of time steps required for the simulation. Throughout this 
% function file, the six degrees of freedom at any particular time step are denoted as: 
% x(1): Lateral Displacement of wheelset 
% x(2): Yaw Displacement of wheelset 
% x(3): Lateral Velocity of wheelset
% x(4): Yaw Velocity of wheelset
% x(5): Lateral Displacement of Left Rail
% x(6): Lateral Displacement of Right Rail

% where x(n) represents the nth column of the solution matrix 'x'.
% The vector of time-derivatives within any time step for the solution vector 'x' has been
% named 'xdot'. Hence, the time-derivative of variable x(n) would be xdot(n).

% Nomenclature:

% Fsuspyw: Lateral suspension force on the wheelset 
% Msuspzw: Vertical suspension moment on the wheelset 
% phi: Wheelset roll angle 
function [xdot]=equations(t,x) 
% Initializing the vector of time-derivatives 
xdot=zeros(6,1); 
% Printing time at end of each time-step on the command screen 
t 
% Obtaining wheelset suspension forces and moments from function 
% 'wheelset_suspension' 
[Fsuspyw,Msuspzw] = wheelset_suspension(x(1),x(3),x(2),x(4)); 
% Invoking function 'wheelset' to solve for wheelset response at each time-step 
[xdot(1),xdot(2),xdot(3),xdot(4),xdot(5),xdot(6),phi]=wheelset(x(1),x(2),x(3),x(4),x(5),x(6),Fsuspyw,Msuspzw);