guidance, flight mechanics and trajectory optimization

variance characterizing Ilt) can be evaluated either from the Fokker*-Planck
equation (also called the forward Kolmogorov equation) on by direct
calculation as follows. Let 2 denote the mean of .% and let v denote
the covariance. Thus
Dffferentiating these two equations, and using Eq. (2.5.29) yields
.
$ =AjbGu
3 =AVt V/ft&
while from Eq. (2.5.31), the boundary conditions
must hold. Thus,the density for ?L is
. with 2 and 3 satisfying Eqs. (2.5.36) and (2.5.37).
Note that
Proceeding with the optimization problem, let
F:-#p--jj
E(z) =E(,&)=.,O
and from Eqs. (2.5.29) and (2.5.36) that
* See Reference (2.5.4)
120
(2.5.36)
(2.5-37)
(2.5-39)
(2.5.40)
(2.5.41)