# MATLAB MATLAB: Trying to understand a MATLAB .m file

#### borjomi

I'm trying to create a paper plane simulation in C and I'm trying to convert MATLAB code to C. Admittedly, I don't know MATLAB (and it's honestly been a while since I've done a lot of math), but I've been able to decode some parts of the following MATLAB code that I found online:

Code:
S		=	0.017;			% Reference Area, m^2
AR		=	0.86;			% Wing Aspect Ratio
e		=	0.9;			% Oswald Efficiency Factor;
m		=	0.003;			% Mass, kg
g		=	9.8;			% Gravitational acceleration, m/s^2
rho		=	1.225;			% Air density at Sea Level, kg/m^3
CLa		=	3.141592 * AR/(1 + sqrt(1 + (AR / 2)^2));
CDo		=	0.02;			% Zero-Lift Drag Coefficient
epsilon	=	1 / (3.141592 * e * AR);% Induced Drag Factor
CL		=	sqrt(CDo / epsilon);	% CL for Maximum Lift/Drag Ratio
CD		=	CDo + epsilon * CL^2;	% Corresponding CD
LDmax	=	CL / CD;			% Maximum Lift/Drag Ratio
Gam		=	-atan(1 / LDmax);	% Corresponding Flight Path Angle, rad
V		=	sqrt(2 * m * g /(rho * S * (CL * cos(Gam) - CD * sin(Gam))));
% Corresponding Velocity, m/s
Alpha	=	CL / CLa;			% Corresponding Angle of Attack, rad

%	Oscillating Glide due to Zero Initial Flight Path Angle
xo		=	[V;0;H;R];
[tb,xb]	=	ode23('EqMotion',tspan,xo);

function xdot = EqMotion(t,x)
%	Fourth-Order Equations of Aircraft Motion

global CL CD S m g rho

V 	=	x(1);
Gam	=	x(2);
q	=	0.5 * rho * V^2;	% Dynamic Pressure, N/m^2

xdot	=	[(-CD * q * S - m * g * sin(Gam)) / m
(CL * q * S - m * g * cos(Gam)) / (m * V)
V * sin(Gam)
V * cos(Gam)];
I've figured out that the 'xdot' function is the key to all of this and I think the first line of xdot (i.e. -CD *q * S, etc) represents the velocity, the second line is the gamma (or flight path angle), the third line is the x position and the last line is the y position.

I've also learned how to solve differential equations using the Runge-Kutta Fourth Order Method. However, when I try to solve for the next timestep using RK4, the values do not correspond with the graphs in MATLAB, which means I'm doing something wrong.

So my questions are, first, am I correct in assuming that the four lines of xdot correspond to velocity, gamma, x position, and y position respectively? If this is true, can I use the velocity and gamma equations to solve for v(n+1) and g(n+1) using the Runge-Kutta method?

I'm sorry for my lack of knowledge, but I hope you can help in answering my question. Please feel free to ask any questions and I'll do my best to clarify.

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