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      FDC help: Vabdot
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    <h2>
      Subsystem <i>Vabdot</i>
    </h2>
    <p><i>Vabdot</i> computes
    time-derivatives of the true airspeed, angle of attack, and side-slip
    angle. It is contained in the block <i><a href="12odes.htm">12
    ODEs</a></i> of the subsystem <i><a href="eqmotion.htm">Aircraft Equations
    of Motion</a></i> in the <i><a href="beaver.htm">Beaver</a></i> model.
    The remaining nine differential equations are stored in the subsystems
    <i><a href="pqrdot.htm">pqrdot</a></i>, <i><a href=
    "eulerdot.htm">Eulerdot</a></i>, and <i><a href=
    "xyhdot.htm">xyHdot</a></i>, which are all contained in <i>12 ODEs</i>.</p>
     <p><b>Note:</b> the time-derivative of the sideslip angle <i>beta</i> that
    leaves <i>Vabdot</i> does not take into account the influence of beta-dot
    itself upon the aerodynamic force along the <i>Y<sub>B</sub></i>-axis. This
    contribution was neglected in the block <i><a href=
    "aeromod.htm">Aeromod</a></i> and has therefore not been included in the
    computed side-force. The resulting error to the time-derivative
    of the state vector, <i>xdot</i>, has been corrected later in the system, by means of the block <i><a
    href="xdotcorr.htm">xdotcorr</a></i>.</p> 
    <h3>
      Inputvector: <i>uvab</i>
    </h3>
<pre>
  uvab = [x&#39; Ftot&#39; Mtot&#39; yhlp&#39;],

  x    = [V alpha beta p q r psi theta phi xe ye H]&#39;     (states)

  Ftot = [Fx Fy Fz]&#39;           (total forces along the body-axes,
                                    computed in the block <a href=
"fmdims.htm">FMdims</a>)

  Mtot = [L M N]&#39;             (total moments along the body-axes,
                                    computed in the block <a href=
"fmdims.htm">FMdims</a>)

  yhlp = [cos(alpha) sin(alpha) cos(beta) sin(beta) ...
          ... tan(beta) sin(psi) cos(psi) sin(theta) ...
          ... cos(theta) sin(phi) cos(phi)]&#39;
            (frequently used sines &amp; cosines, coming from <a href=
"hlpfcn.htm">Hlpfcn</a>)


  V    : airspeed [m/s]
 {alpha: angle of attack [rad]                                  }
 {beta : sideslip angle [rad]                                   }
  p    : roll rate [rad/s]
  q    : pitch rate [rad/s]
  r    : yaw rate [rad/s]
 {psi  : yaw angle [rad]                                        }
 {theta: pitch angle [rad]                                      }
 {phi  : roll angle [rad]                                       }
 {xe   : x-coordinate in Earth-fixed reference frame [m]        }
 {ye   : y-coordinate &#39;&#39;     &#39;&#39;          &#39;&#39;      &#39;&#39;  [m]        }
 {H    : altitude above sea-level [m]                           }

  Fx, Fy, Fz: total forces along the aircraft&#39;s body-axes [N]
 {L, M, N   : total moments along the aircraft&#39;s body-axes [Nm] }
</pre>
    <p>The inputvariables which are not actually used by <i>Vabdot</i> have been
    displayed between brackets. Of the inputvector <i>yhlp</i>,
    <i>cos(alpha)</i>, <i>cos(beta)</i>, <i>sin(alpha)</i>, <i>sin(beta)</i>,
    and <i>tan(beta)</i> are used.</p> 
    <h3>
      Outputvector: <i>yvab</i>
    </h3>
<pre>
  yvab = [Vdot alphadot betadot]&#39;

  Vdot    : dV/dt [m/s^2]
  alphadot: d(alpha)/dt [rad/s^2]
  betadot : d(beta)/dt [rad/s^2]
</pre>
    <p>Note: the beta-dot equation in <i>Vabdot</i> does <i>not</i> take into
    account the contribution of beta-dot itself to the sideforce
    <i>F<sub>y</sub></i>. Corrections are made in <i><a href=
    "xdotcorr.htm">xdotcorr</a></i>.</p> 
    <h3>
      Parameters to be defined in the Matlab workspace
    </h3>
    <ul>
      <li>
        <i>GM1</i>: vector with some important geometrical properties of the
        &#39;Beaver&#39; aircraft, and the mass of the aircraft (which is
        assumed to be constant during the motions of interest). Here, the mass
        of the aircraft is extracted from <i>GM1</i>. <i>GM1</i> can be loaded
        into the Matlab workspace by calling the routine <i><a href=
        "datload.htm">DATLOAD</a></i>. If the necessary datafile with aircraft
        model parameters does not yet exist, run <i><a href=
        "modbuild.htm">MODBUILD</a></i> first.
      </li>
    </ul>
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