guidance, flight mechanics and trajectory optimization

2.2.1.1 Manual Rendezvous Guidance
The technique of fixing the direction of the line of sight in inertial
space effectively uncouples the linear and angular motion and reduces the
problem to one dimension. This feature is a particularly useful in the case
where a pilot is manually performing the rendezvous. Such a system is con-
sidered as a back-up for the Gemini missions (Reference 2.3); for the Gemini
scheme, the pilot visually observes the relative motion between the spacecraft
and the target vehicle with respect to a star background. Range and range-
rate information are provided by radar or optical means. When the two ve-
hicles are within a preselected distance, the pilot initiates a thrust
maneuver normal to the line of sight until he observes that the relative
(angular) motion has been eliminated. This process is continued throughout
the rendezvous whenever relative motion is again noticed. The range and
rate range are monitored so that the time to begin the braking maneuver can
be determined.
2.2.1.2 Separation of Guidance-Navigation Tasks
In the previous section, the astronaut performing the rendezvous maneuver
was required to navigate (i.e., determine when the relative motion has ceased)
during periods of thrust application. A technique developed by Steffan
(Reference 2.4) determines the time duration of the thrusting from data taken
before thrust initiation. The angular rate of the LOS is allowed to oscillate
between limits with the period of oscillation determined by thrusting in the
LOS direction. This technique requires the application of several velocity
increments normal to the LOS, the times of these applications are related to
the period of the limit cycle and are controlled by controlling the range
rate. The desired period of the limit cycle is then chosen so that the time
between corrections is sufficient to allow for data taking and processing.
This time will vary depending on how the data is being taken and processed,
e.g., a range radar feeding information directly to a computer vs. optical
measurements and hand calculations by an astronaut.
By the use of the rocket motor normal to the LOS, the rendezvous ve-
hicle is established on a collision course with the target vehicle such that
the direction of the LOS is stabilized, to within some limits, in inertial
space. The approximate behavior of this limit cycle can be determined
analyzing the expressions for the angular rate of the LOS as a function of
time for (1) termination of normal thrust and (2) time for the initiation of the
normal thrust. First the case of no thrust is considered.
A polar coordinate system will be used to describe the motion. In this
system, the range (p) is defined as the distance from the rendezvous vehicle
to the target vehicle; a' is measured from an inertial reference direction;
and the origin of the coordinate system is at the target vehicle.
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