## Subsystem xyHdot

xyHdot, which is contained in the subsystem 12 ODEs of Aircraft Equations of Motion (Beaver) within the Beaver model, computes time-derivatives of the coordinates xe and ye and the altitude H.

The remaining nine differential equations are stored in the subsystems Vabdot, pqrdot, and Eulerdot, which are all contained in 12 ODEs.

### Inputvector: uxyh

     uxyh = [x' Ftot' Mtot' yhlp'], and [u+uw  v+vw  w+ww]'.

     x    = [V alpha beta p q r psi theta phi xe ye H]'     (states)

     Ftot = [Fx Fy Fz]'           (total forces along the body-axes,
                                       computed in the block FMsort)

     Mtot = [L M N]'             (total moments along the body-axes,
                                       computed in the block FMsort)

     yhlp = [cos(alpha) sin(alpha) cos(beta) sin(beta) ...
             ... tan(beta) sin(psi) cos(psi) sin(theta) ...
             ... cos(theta) sin(phi) cos(phi)]'
              (frequently used sines & cosines, computed in Hlpfcn)

     [u+uw v+vw w+ww]' = [u v w]' + [uw vw ww]' = ybvel + uwind(1:3)

ybvel is computed in the masked subsystem block uvw, uwind is an external inputvector with atmospheric disturbances.

    {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 ''     ''          ''      ''  [m]        }
    {H    : altitude above sea-level [m]                           }

    {Fx, Fy, Fz: total forces along the aircraft's body-axes [N]   }
    {L, M, N   : total moments along the aircraft's body-axes [Nm] }

     u    : component of the airspeed V along the XB-axis [m/s]
     v    : component of the airspeed V along the YB-axis [m/s]
     w    : component of the airspeed V along the ZB-axis [m/s]
     uw   : component of wind + turbulence along XB-axis [m/s]
     vw   : component of wind + turbulence along YB-axis [m/s]
     ww   : component of wind + turbulence along ZB-axis [m/s]

The inputvariables which are not actually used by xyHdot have been displayed between curly braces.

### Outputvector: yxyh

     yxyh = [xdot ydot Hdot]'

     xdot = d(xe)/dt [m/s]
     ydot = d(ye)/dt [m/s]
     Hdot = dH/dt [m/s]