📄 eulerdot.htm
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<TITLE>FDC help: Eulerdot</TITLE>
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<H2>Subsystem <I><FONT FACE="Arial","Helvetica","Sans Serif">Eulerdot</FONT></I></H2>
<I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif">Eulerdot</FONT></I> is a masked S<SMALL>IMULINK</SMALL> subsystem, which contains the equations to calculate time derivatives of the Euler angles <I>psi</I>, <I>theta</I>, and <I>phi</I>. The block <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif">Eulerdot</FONT></I> is contained in the sub-sub-system <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif"><A HREF="12odes.htm">12 ODEs</A></FONT></I> of the subsystem <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif"><A HREF="eqmotion.htm">Aircraft Equations of Motion</A></FONT></I> in the S-function <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif"><A HREF="beaver.htm">Beaver</A></FONT></I>. The remaining nine differential equations are stored in the subsystems <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif"><A HREF="vabdot.htm">Vabdot</A></FONT></I>, <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif"><A HREF="pqrdot.htm">pqrdot</A></FONT></I>, and <FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif"><I><A HREF="xyhdot.htm">xyHdot</A></I></FONT>, which are all contained in <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif">12 ODEs</FONT></I>.
<H3>Inputvector: <I>ueul</I>
</H3>
<PRE> 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 <A HREF="fmsort.htm">FMsort</A>)
Mtot = [L M N]' (total body-axes moments,
computed in <A HREF="fmsort.htm">FMsort</A>)
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 <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 '' '' '' '' [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] }
</PRE>
The inputvariables which are not actually used by <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif">Eulerdot</FONT></I> have been displayed between accolades. Of the inputvector <I>yhlp</I>, <I>sin(phi)</I>, <I>cos(phi)</I>, <I>sin(theta)</I>, and <I>cos(theta)</I> are used.
<H3>Outputvector: <I>yeul</I>
</H3>
<PRE> yeul = [psidot thetadot phidot]'
psidot, thetadot, phidot: time derivatives of the Euler angles [rad/s^2].
</PRE>
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