LinOrb:

Path: Orbit/RHSOrbit

% Computes the linearized orbit equations. 
   To get normalized equations with nt as the independent variable, just 
   set n = 1. Pass x as empty to get the state equations. If dT is entered it 
   will generate the discrete time equations

   y      = c*x[k] + d*u[k]
   x[k+1] = a*x[k] + b*u[k]

   otherwise

   y      = c*x + d*u
   dx/dt  = a*x + b*u

--------------------------------------------------------------------------
   Form:
   xD           = LinOrb( x, n, aD )
   [a, b, c, d] = LinOrb( [], n, [], dT )
--------------------------------------------------------------------------

   ------
   Inputs
   ------
   x                (6,1) state [dr;rtheta;z;ddr/dt;drtheta/dt;dz/dt]
   n                (1,1) orbit rate
   aD               (3,1) acceleration vector
   dT               (1,1) time step

   -------
   Outputs
   -------
   a                (6,6) State transition matrix or (6,1) state derivative
   b                (6,3) Input matrix
   c                (3,6) Output matrix (position)
   d                (3,3) Feedthrough matrix

--------------------------------------------------------------------------
	  References:   Kaplan, M., Modern Spacecraft Dynamics and Control, p. 111.
                 Valado, D., Fundamentals of Astrodynamics and Applications, 
                 pp. 348-51.
--------------------------------------------------------------------------

Back to the Orbit Module page