guidance, flight mechanics and trajectory optimization

In this form the equations are valid to the second order in the e . It is seen
that the truncation of an infinite series (K) is required in only the radial
and the binormal component equations.
As already indicated, however, a linear theory is usually adequate for
rendezvous discussions; therefore, these equations reduce to the following set
of linear equations:
2-
where t7 -/a
-3
. 1.13
Here the independent variable is time; and as is customary, the dot indicates
differentiation with respect to time.
The first important point to note is that the out-of-plane motion is
decoupled from the in-plane motion, a feature that is characteristic of all
linear sets. These equations can be changed so that the independent variable
is the mean anomaly, M, since dM = n dt. This step is equivalent to making
the unit of time equal to the time required for a change ofoone radian in mean
anomaly. The resulting equations are (where the open dot is used to indicate
d/dM):
A major simplification occurs if the independent variable is changed to
the true anomaly, (@I, or to the argument of latitude (0 = 8 + 0,). The
transformation makes use of the conservation of angular momentum
8
1.12
1.14a
1.14b