guidance, flight mechanics and trajectory optimization

This updating can be accomplished, however, at a much slower rate than is
necessary for steering and cut-off calculations. In the reference, Gunckel
proposes to update one element of the matrix each computation cycle; thus,
updating the complete matrix in nine cycles. Since the quantities under the
integral sign are taken to be constant during the time period, the above
equation can be written as
2.2.4.2 Two Impulse Rendezvous
The first linear impulsive guidance scheme to be considered was pre-
pared by Clohessy and Wiltshire (Reference 2.1) and is the basis of the
Gemini automatic rendezvous guidance (Reference 2.2 and 2.3). Two major
velocity impulses are used through several smaller mid-course corrections
calculated from the same equations and based on intermediate measurements of
the state attained by the first change in velocity may also be required.
The first velocity impulse is applied at the beginning of the rendezvous
maneuver and establishes the target and rendezvous vehicle on a collision
course. The second impulse is required to null the range rate at the time
of closure. Consider a target
vehicle in a circular orbit and
a coordinate system fixed to the
target such that the Y axis is
always along the radius from
the center of attraction, the
X axis is circumferential inthe
direction of the motion of
the target, and the Z axis
completes the right handed
XYZ set. If the rendezvous
vehicle is in an orbit which
closely approximates that of
the target vehicle, then the
transition matrix of Equation
(1.58) can be used to describe VEHICU
the relative motion. In this Linear Rendezvous Coordinate System
I scheme, the only concern is the Figure 2.5
reduction of the range to zero;
thus, the only part of the matrix which is needed is rewritten below.
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