I know absolutely nothing about MATLAB, but I do know about orbital elements.
This gives the format of two-line elements – what each element means.
http://celestrak.com/NORAD/documentation/tle-fmt.shtml
The fourth element is the epoch time. In other words, the satellite was in the position given by the elements at the time specified by the epoch time.
The first derivative, second derivative, and B*star are for orbit propagation. They define atmospheric drag characteristics of the satellite. To actually predict where the satellite will be in the future, you need these, but that’s something you add on to your program (or spreadsheet, in my case) after you’ve got the basics down.
The second line contains info on the satellite’s position and velocity. Three of the elements fix the satellite’s position and velocity within the orbital plane (mean motion, eccentricity, and mean anomaly). Three rotate the satellite’s position and velocity from a perifocal coordinate system (position/velocity within the orbital plane) to the geocentric equatorial coordinate system (the satellite’s position and velocity relative to the center of the Earth (right ascension, inclination, argument of perigee).
You have two of the second line elements that have to be changed right off the bat. If you know Kepler’s third law, you can calculate the semi-major axis from the mean motion. Mean motion in your two-lines are expressed in revolutions/day instead of radians/second, so you have to convert the units to radians/second. The true anomaly is needed instead of the mean anomaly. This is a two step method, normally using the Newton-Raphson method to go from mean anomaly to eccentric anomaly (there is no analytic solution – you have to use a trial and error method to solve the equation), then using a more standard analytic equation to go from eccentric anomaly to true anomaly.
If you don’t care about understanding how you get from two-lines to geocentric coordinates, you can do it in about 6 equations. If you want to understand what’s happening, you need a book’s worth of equations so you can step things through one step at a time. As enigma kind of hinted at, knowledge of orbital mechanics and an ability to express oneself coherently seem to be mutually exclusive talents.
Angles are expressed in greek letters, linear numbers in western letters.
a= semi-major axis
p= semi-latus rectum, or p=a(1-e^2)
r= satellite radius (the velocity is wholly dependent on the satellite's position, so you never see the velocity in the equations)
\Theta or Theta (with a capital letter) is the sum of argument of perigee and true anomaly (i.e. - the satellite's location along the orbital ellipse relative to the equator)
\nu or nu is the true anomaly
\iota or i is the inclination
\Omega or Omega (with a capital letter) is right ascension of ascending node
\omega or omega (with a small letter) is argument of perigee
\tau or tau is usually orbital period
All the definitions depend on the book you happen to be using, but these are the most common.
x=r(cos\Theta cos\Omega - sin\Theta sin\Omega sin\iota)
y=r(cos\Theta sin\Omega + sin\Theta cos\Omega cos\iota)
z=r(sin\Theta sin\iota)
\Theta = \omega + \nu
\dot x = - \sqrt{\frac{\mu}{p}} [cos\Omega \left(sin \Theta + e sin \omega) + sin \Omega cos \iota (cos \Theta + e cos \omega)]
\dot y = - \sqrt{\frac{\mu}{p}} [sin\Omega \left(sin \Theta + e sin \omega) - cos \Omega cos \iota (cos \Theta + e cos \omega)]
\dot z = \sqrt{\frac{\mu}{p}}[sin \iota ( cos \Theta + e cos \omega)]
\mu is the geocentric gravitational constant (3.986 x 10^5 km^3/sec^2)