📄 uvwdot.hlp
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UVWDOT is a masked Simulink subsystem, which is contained in the
subsystem 'Additional Outputs' from the S-function BEAVER. UVWDOT
computes time-derivatives of the body-axes velocity components u,
v, and w. It is an additional OUTPUT block, which is NOT needed
to solve the state equations themselves! In the system BEAVER,
the true airspeed V, angle of attack alpha, and sideslip angle
beta have been used as state variables in stead of u, v, and w!
Nowhere in the system BEAVER, time-derivatives of the body-axes
velocities are integrated; therefore, UVWDOT may be deleted from
the system BEAVER 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' should 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
blocks UVW and UVWDOT both contain output equations only, and
neither one of them uses the outputs from the other. The outputs
from UVW are necessary for solving the state equations; the outputs
from UVWDOT are not.
Inputvectors: x, xdot, and yhlp (the inputvariables which are
not actually used by UVWDOT are displayed between accolades).
=============================================================
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)
where:
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] }
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]')
where:
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]
More info:
==========
UVWDOT is an additional output block, which is not needed to
solve the state equations. It uses the outputs from the subsystem
'Aircraft Equations of Motion' as inputvectors, and it is, of
course, closely related to the time-derivatives of the other
state variables. See therefore EQMOTION.HLP, 12ODES.HLP, VABDOT.HLP,
PQRDOT.HLP, EULERDOT.HLP, and XYHDOT.HLP for more info. See also
UVW.HLP. Consult HLPFCN.HLP for more info about the vector yhlp.
See MOREOUTS.HLP for details about the subsystem 'Additional
Outputs'.
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The FDC toolbox, Copyright Marc Rauw 1994-1998.
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