guidance, flight mechanics and trajectory optimization

This equation ;zill have a solution for positive time, if 4'0 and IAd\ pp6 .
If these conditions are not met, or if the time to rendezvous is unsuitable,
a velocity impulse along the line of sight can be added to remedy the
situation.
The solution to the Equations (2.9) for an acceleration is applied along
the line of sight (uR) is now
If the conditions for rendezvous (i.e., P =o, p = 0) are inserted in
these equations, it can be seen that a solution can be obtained for a,
equal to a constant. Thus, the rocket motor A~rn+sh~nrr thrust along the line
of sight need not be throttleable. However, the normal thrust motor must
furnish thrust according to
and is therefore required to be throttleable.
The author or Reference (2.5) compares this scheme to a scheme which
nulls the angular rate similar to that described in the last section. The
comparison indicated that the coriolis balance technique requires a lower
thrust level for both the range and normal rocket motors; however, the total
impulse and flight time are greater.
2.2.3 Improved Model - The Inclusion of a Gravity Gradient
An improvement in the description of the gravity model can be made which
will increase the range of initial conditions over which the preceding methods
are valid, yet still retain the simple expressions for determining the
duration of thrusting. The improved gravity model consists of approximating
the difference in the gravitational acceleration of the two vehicles ( A$ )
by
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