guidance, flight mechanics and trajectory optimization

Figure 2.1
Polar Coordinate System
(Since the out-of-plane motion is uncoupled, only motion in two dimensions
is considered.) Now, since for the case under consideration, there is no
relative acceleration between the two vehicles due to the gravity gradient;
thus the angular momentum of the system will remain constant (for period of
no thrust). i.e.,
The subscript, o, refers to some initial time. Therefore, if the normal
control has been operating, the velocity vector will lie along the line of
sight (to the first order) and the range as a function of time will be
With the use of this expression for range, the angular momentum equation can
be written as
2
sw (,+$t)?
Equation (2.3) is the desired relation for the angular rate ( b ) of the
LOS for periods of free motion.
32
0
(2.1)
(2.3)