NonDimensionalOrbit:

Path: Orbit/OrbitMechanics

% Dimensionalize or non-dimensionalize an orbit.
   dir determines the direction. dir = 0 or dir omitted
   will non-dimensionalizes r, v, t and mu. r, v and t may be vectors.

   We non-dimesionalize as follows:

   Quantity	Units       Nondimensionalizing Constanst
   r           [L]         rRef
   t           [T]         rRef/sqrt(mu/rRef)
   v           [L/T]       sqrt(mu/rRef)
   mu          [L^3/T^2]	mu
   accel       [L/T^2]     mu/rRef^2

   sqrt(mu/r) = v = L/T so we pick T = rRef/sqrt(mu/r)

   Non-dimensional units are often better for estimation and optimization.
   For circular orbits the nominal orbit radius is best for rRef. For
   other orbits, such as a geosynchronous transfer orbit you can pick
   the mean orbit. When using nondimensional units you must 
   non-dimensionalize the external accelerations by multiplying by
   fAcc.

   Type NonDimensionalOrbit for a simulation of a circular planar orbit
   at 1 AU from the sun. It will plot non-dimensional and dimensional
   units. In non-dimensional units r and v will oscillate between +/- 1.

   Since version 2014.1
--------------------------------------------------------------------------
   Form:
   [r, v, t, mu, fAcc] =  NonDimensionalOrbit( r, v, t, mu, rRef, dir )
--------------------------------------------------------------------------

   ------
   Inputs
   ------
   r       (3,:)   Position vectors
   v       (3,:)   Velocity vectors
   t       (1,:)   Time vector
   mu      (1,1)   Gravitational constant
   rRef	(1,1)   Reference length
   dir     (1,1)   0 or no input means non-dimensionalize

   -------
   Outputs
   -------
   r       (3,:)   Position vectors
   v       (3,:)   Velocity vectors
   t       (1,:)   Time vector
   mu      (1,1)   Gravitational constant
   fAcc    (1,1)   Acceleration scaling

--------------------------------------------------------------------------

Children:

Common: Database/Constant
Common: Graphics/Plot2D
Common: Graphics/TimeLabl
Math: Integration/RK4
SC: BasicOrbit/Period
SC: BasicOrbit/RHSOrbit

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