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      FDC help: xdotcorr (Beaver)
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    <h2>
      Subsystem <i>xdotcorr (Beaver)</i>
    </h2>
    <p><i>xdotcorr (Beaver)</i> converts implicit state equations of the &#39;Beaver&#39; dynamic model into explicit state equations. It is contained
    in the subsystem <i><a href="eqmotion.htm">Aircraft Equations of Motion
    (Beaver)</a></i> in the <i><a href="beaver.htm">Beaver</a></i> model; being the only aircraft-dependent block of this subsystem. In
    this case, <i>xdotcorr</i> depends upon the aerodynamic model of the DHC-2
    &#39;Beaver&#39; from <a href="#Tjee&amp;Mulder">ref.[1]</a>. </p>
    <p>The implicitness of the original state equations
    is caused by a contribution of the time-derivative of beta-dot to the
    aerodynamic sideforce. Since Simulink can not always cope with implicit
    ODEs, the ODEs were divided in an aircraft-independent part and a separate
    correction term. It is this correction term which has been implemented in
    <i>xdotcorr (Beaver)</i>.</p> 
     <p><i>xdotcorr</i> can be adapted for other aircraft models, in cases where
    it is necessary to bring into account contributions of time-derivatives of
    states to the aerodynamic forces and/or moments, which would otherwise
    result in implicit state equations. Such implicit state equations most
    often involve alpha-dot and beta-dot terms.</p> 
    <h3>
      Inputvectors for <i>xdotcorr (Beaver)</i>
    </h3>
<pre>
 xdot = dx/dt = [Vdot alphadot betadot pdot qdot rdot ...
                 psidot thetadot phidot xedot yedot Hdot]&#39;
       (state derivatives, without corrections which make impli-
          cit equations explicit, coming from subsystem <a href=
"12odes.htm">12 ODEs</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>)

 yatm = [rho ps T mu g]&#39;,  (atmospheric properties, computed in
                                              the block <a href=
"atmosph.htm">Atmosph</a>)


{Vdot    : time-derivative of airspeed [m/s^2]                 }
{alphadot: time-derivative of angle of attack [rad/s]          }
 betadot : time-derivative of sideslip angle [rad/s]
                                               (uncorrected!)
{psidot  : time-derivative of yaw angle [rad/s]                }
{thetadot: time-derivative of pitch angle [rad/s]              }
{phidot  : time-derivative of roll angle [rad/s]               }
{pdot    : time-derivative of roll rate [rad/s^2]              }
{qdot    : time-derivative of pitch rate [rad/s^2]             }
{rdot    : time-derivative of yaw rate [rad/s^2]               }
{xedot   : time-derivative of x-coordinate in Earth-fixed
                                        reference frame [m/s]  }
{yedot   : time-derivative of y-coordinate in Earth-fixed
                                        reference frame [m/s]  }
{Hdot    : time-derivative of altitude above sea-level [m/s]   }

 rho  : airdensity [kg/m^3]
{ps   : static pressure [N/m^2]                                }
{T    : temperature [K]                                        }
{mu   : dynamic viscosity [kg/(m*s)]                           }
{g    : acceleration of gravity [m/s^2]                        }
</pre>
    <p>The inputvariables which are not used by <i>xdotcorr</i> have been put
    between curly braces. Of the vector <i>yhlp</i>, only <i>cos(beta)</i> is
    used.</p> 
    <h3>
      Outputvector of <i>xdotcorr</i>
    </h3>
<pre>
 xdot = [Vdot alphadot betadot pdot qdot rdot psidot ...
         ... thetadot phidot xedot yedot Hdot]&#39;

 (xdot with correction for beta-dot influence upon sideforce Ya)
</pre>
    <p>Here, <i>betadot</i> has been corrected for the beta-dot influence upon the
    aerodynamic sideforce <i>Y<sub>a</sub></i>! </p>
    <h3>
      Parameters which must be set in the Matlab Workspace
    </h3>
    <ul>
      <li>
        <i>AM</i>: matrix with stability and control derivatives (currently
        valid for the nonlinear aerodynamic model of the DHC-2
        &#39;Beaver&#39;, see <a href="#Tjee&amp;Mulder">ref.[1]</a>). The
        stability derivative <i>CYbdot</i> is extracted from this matrix to
        determine the influence of beta-dot upon aerodynamic sideforce
        <i>Y<sub>a</sub></i>.
      </li>
      <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). In
        <i>xdotcorr</i>, the wing span <i>b</i>, wing area <i>S</i>, and mass
        <i>m</i> are extracted from <i>GM1</i>.
      </li>
    </ul>
    <p>The vector GM1 and the matrix AM can be loaded into the workspace from file
    by applying the routine <i><a href="datload.htm">DATLOAD</a></i>. Run <i><a
    href="modbuild.htm">MODBUILD</a></i> first if this datafile does not yet
    exist.</p> 
    <h3>
      <a name="Tjee&amp;Mulder">References</a>
    </h3>
    <ol>
      <li>
        R.T.H. Tjee and J.A. Mulder: <i><font color="#505050">Stability and
        Control Derivatives of the De Havilland DHC-2 &quot;Beaver&quot;
        aircraft</font>. Report LR-556, Delft University of Technology, Delft,
        The Netherlands, 1988.</i>
      </li>
    </ol>
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