BilinearTangentAltitude:

Path: SCPro/Landers

% Bilinear tangent law for maximizing altitude on launch.
   We assume the vehicle is constant and the final time is known.

   Assumes constant acceleration. The model is in a cartesian frame
   with gravity constant and in the negative y direction.

   The boundary conditions are for the x velocity to equal the orbital
   velocity and the y velocity to be zero.

   If the ratio of rocket acceleration to gravity is too low you cannot
   achieve a circular orbit. In that case the cost will be high. The 
   result will be a non-zero radial velocity. This will depend on the
   initial x and y velocities.

   Type BilinearTangentAltitude for a demo for an upper stage with
   a rocket engine capable of 1.5 g.

   This routine uses fminsearchbnd which is freely available on the web.

   Since version 2014.1
--------------------------------------------------------------------------
   Form:
   [beta, yF, cost] = BilinearTangentAltitude( d, t )
--------------------------------------------------------------------------

   ------
   Inputs
   ------
   d       (1,1)	Data structure
                   .mu     (1,1) Gravitational constant
                   .r      (1,1) Initial radius
                   .u      (1,1) Initial x velocity
                   .v      (1,1) Initial y velocity
                   .thrust (1,1) Engine thrust
                   .mass   (1,1) Mass
                   .tF     (1,1) End time for the burn
                   .opt	(1,1) fminsearch options
   t       (1,:)	Time vector for beta

   -------
   Outputs
   -------
   beta    (1,:)	Thrust angle from horizontal
   yF      (1,1)   Altitude
   cost    (1,1)   Final cost

--------------------------------------------------------------------------
   Reference: Arthur E. Bryson, Jr., Y. C. Ho, "Applied Optimal Control:
              Optimization, Estimation, and Control," Orbit, pp. 83-86.
--------------------------------------------------------------------------

Children:

Propulsion: Rocket/MassEquivalentDV
Common: CommonData/SwooshWatermark
Common: General/CellToMat
Common: General/MatToCell
Common: General/Watermark
Common: Graphics/NewFig
Common: Graphics/Plot2D
Common: Graphics/PltStyle
Common: Graphics/TimeLabl
Math: Integration/RK4

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