## Subsystem Eulerdot

Eulerdot contains the equations to calculate time derivatives of the Euler angles psi, theta, and phi. The block Eulerdot is contained in the subsystem 12 ODEs, which itself is contained in Aircraft Equations of Motion within the Beaver model. The remaining nine differential equations are evaluated in the subsystems Vabdot, pqrdot, and xyHdot, which are all contained in 12 ODEs.

### Inputvector: ueul

      ueul = [x' Ftot' Mtot' yhlp'],

      x    = [V alpha beta p q r psi theta phi xe ye H]'     (states)
      Ftot = [Fx Fy Fz]'                     (total body-axes forces,
                                                  computed in FMsort)
      Mtot = [L M N]'                       (total body-axes moments,
                                                  computed in FMsort)
      yhlp = [cos(alpha) sin(alpha) cos(beta) sin(beta) ...
              ... tan(beta) sin(psi) cos(psi) sin(theta) ...
              ... cos(theta) sin(phi) cos(phi)]'
                              (sines and cosines, computed in Hlpfcn)

     {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] }

The inputvariables which are not actually used by Eulerdot have been displayed between curly braces. Of the inputvector yhlp, sin(phi), cos(phi), sin(theta), and cos(theta) are used.

### Outputvector: yeul

      yeul = [psidot thetadot phidot]'

      psidot, thetadot, phidot: time derivatives of the
                                Euler angles [rad/s^2].