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    <title>
      FDC help: uvw
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    <h2>
      The subsystem <i>uvw</i>
    </h2>
    <p>The block <i>uvw</i> computes the body-axes velocities <i>u</i>, <i>v</i>, and <i>w</i>. The body-axes velocity components must be known to solve the state-equations for the coordinates <i>x<sub>e</sub></i>, <i>y<sub>e</sub></i>, and the altitude <i>H</i>, so even though <i>u</i>, <i>v</i>, and <i>w</i> have been replaced by the true airspeed <i>V</i>, angle of attack <i>alpha</i>, and sideslip angle <i>beta</i> as state variables, it is not allowed to delete this block from the aircraft model!</p>
    <p>The outputs from <i>uvw</i> are used by the block <i><a href=
    "xyhdot.htm">xyHdot</a></i> in the subsystem <i><a href="12odes.htm">12&nbsp;ODEs</a></i>. <i>uvw</i> is included in the subsystem <i><a href=
    "eqmotion.htm">Aircraft Equations of Motion</a></i> of the <i><a href="beaver.htm">Beaver</a></i> model.</p>
     <p>Since <i>u</i>, <i>v</i>, and <i>w</i> are not state variables, their
    time-derivatives do not have to be known to solve the equations of motion.
    However, for some purposes, knowledge of these time-derivatives still may
    be useful; therefore, a separate block <i><a href=
    "uvwdot.htm">uvwdot</a></i> has been included in the subsystem <i><a href=
    "moreouts.htm">Additional Outputs</a></i> within the <i>Beaver</i> model.</p> 
    <h3>
      Inputvectors: <i>x</i> and <i>yhlp</i>
    </h3>
<pre>
  x    = [V alpha beta p q r psi theta phi xe ye H]&#39;     (states)

  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 and 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]                           }
</pre>
    <p>The inputvariables which are not actually used by the block <i>uvw</i> have
    been displayed between curly braces. From <i>yhlp</i> the signals
    <i>cos(alpha)</i>, <i>cos(beta)</i>, <i>sin(alpha)</i> and <i>sin(beta)</i>
    are used.</p> 
    <h3>
      Outputvector: <i>ybvel</i> (bvel = &#39;body-axes velocities&#39;)
    </h3>
<pre>
  ybvel = [u v w]&#39;,

  u     : component of the true airspeed V along XB-axis [m/s]
  v     : component of the true airspeed V along YB-axis [m/s]
  w     : component of the true airspeed V along ZB-axis [m/s]
</pre>
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