## Subsystem uvwdot

The block uvwdot, which is contained in the subsystem Additional Outputs from the Beaver model, computes time-derivatives of the body-axes velocity components u, v, and w.

uvwdot is an additional output block, which is not needed to solve the state equations themselves, because the true airspeed V, angle of attack alpha, and sideslip angle beta have been used as state variables for the aircraft model, instead of u, v, and w! Nowhere in the Beaver model time-derivatives of the body-axes velocities are sent through an integrator block or used by other blocks which are necessary to solve the equations of motion; therefore, uvwdot can be deleted from the Beaver model without affecting the solution of the equations of motion.

Note: contrary to uvwdot, the block uvw which is contained in the subsystem Aircraft equations of motion may not be removed from the system, because the outputs from that block (u, v and w) are needed in order to compute the aircraft's coordinates.

The equations in uvwdot are, of course, closely related to the time-derivatives of the other state variables. See therefore the descriptions of the subsystems Aircraft Equations of Motion, 12 ODEs, Vabdot, pqrdot, Eulerdot, and xyHdot for more information.

### Inputvectors: x, xdot, and yhlp

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

      xdot = dx'/dt                 (time derivative of state vector)

      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 and cosines, coming from 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]                           }

The inputvariables which are not actually used by uvwdot have been displayed between curly braces. Of the vector xdot, the time derivatives of V, alpha, and beta are used; from yhlp, cos(alpha), sin(alpha), cos(beta), and sin(beta) are extracted.

### Outputvector: yuvw

      yuvw = [udot vdot wdot]' = d/dt([u v w]')

      u    : velocity component along the XB (body-) axis [m/s]
      v    : velocity component along the YB axis [m/s]
      w    : velocity component along the ZB axis [m/s]