guidance, flight mechanics and trajectory optimization

Denoting d/d6 by the prime, ', there finally results:
For the case of coast arcs when al = a2 = a3 = 0, it is to be noted that the
out-of-plane motion is simple harmonic In terms of true anomaly and that the
first integral for the circumferential equation can be written down at once.
Another form of the linear equations of motion which will be considered
makes use of the eccentric anomaly, E, as the independent variable. To
accomplish this transformation, the substitution
is made where q = 1 - e eoe E = 'l/aT and u = -6-z
where
with the asterisk, R ) there results:
equals the acceleration of gravity at the distance of the semi-major axis. For
coast arcs the third equation is easily integrable as will be shown below, and
the second equations possess an immediate integral as for Figure 1.16.
9
1.16a
1.16b
1.16~
1.17
1.18a
1.18b
1.18~