guidance, flight mechanics and trajectory optimization

2.1.3 Approximate Equations
On the other hand, one may choose to obtain a set of linear
equations for the components of 4 which may be chosen in order
differential
to develop a
more accurate representation. This procedure will be adopted; but at the outset
it is desirable to point out that solutions to the homogenous part of
equations (i.e., for the case with no force, 01 that will be obtained are, in
fact, already essentially available. These are the state transition matrices
which have been discussed in the State Determination and/or Estimation
Monograph (Reference 1.1). Of course, independent '
variable changes and simple
coordinate changes will be necessary in order to obtain all the various forms
that may be used.
2.1.3.1 Angular Forms of the Equations
43
.
The expression for 2 = Y - 5 is developed in terms of r 1' 8, t,, 82,
and their derivatives by making use of
k=&, ~=64+$,_v, g =-bg , *ad -v =-(e'+ $ ),u. 1.9
The gravitational terms, expressed in components along g, x9 and W, me
The motion of the target satellite can be shown to satisfy
7
1.8
1.10
l.llb
l.llc