AirshipIntegrals:

Path: Airships/Modeling

% Compute the geometric integrals for a double-ellipsoid airship hull.
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   Form:
   [I1, I3, J1, J2] = AirshipIntegrals( a1, a2, b, hullFraction, xo );
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   ------
   Inputs
   ------
   a1            (1)       Semi-major axis of front ellipsoid   [m]
   a2            (1)       Semi-major axis of rear ellipsoid    [m]
   b             (1)       Semi-minor axis of each ellipsoid    [m]
   hullFraction  (1)       Fraction of total length regarded as hull
                             (point from nose at which fins begin)
   xo            (1)       x-Location of body-frame origin      [m]
                             (measured back from nose)

   -------
   Outputs
   -------
   I1            (1)       Integral of (dA/dx) from nose to hull length / (vol)^(2/3)
   I3            (1)       Integral of x*(dA/dx) from nose to hull length / L*(vol)^(2/3)
   J1            (1)       Integral of 2*r from nose to hull length / (vol)^(2/3)
   J2            (1)       Integral of 2*r*x from nose to hull length / L*(vol)^(2/3)

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   Reference: Jones, DeLaurier, "Aerodynamic Estimation Techniques for
              Aerostats and Airships", AIAA Lighter-than-Air Systems
              Conference, Anapolis MD, 1981, Paper No. 81-1339.
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   Copyright (c) 2003 Princeton Satellite Systems, Inc.
   All rights reserved.
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