guidance, flight mechanics and trajectory optimization

This equation may now be solved forp,
lower limit)
and replacing rm by 2-,,, (the desired
Thus, for the case when the initial slope '$ is negative the motor is fired
whenever this equation is satisfied and firing is terminated whenever
T- t ~mor . If this scheme is used to control the velocity along
the line of sight, the time until rendezvous will remain between the limits
f -,- and Ge and the range will be forced to decrease approximately ex-
ponentially with time. As the range becomes sufficiently small, the range
rate control loop is opened and a docking maneuver initiated.
2.2.2 Coriolis Balance
The two previous sections considered guidance schemes based on nulling
the angular rate of the line of sight. In this section, a technique where
the line of sight is allowed to rotate at a constant rate is considered. It
will be seen that this restriction is equivalent to requiring that the force
normal to the line of sight be equal to the coriolis acceleration. Hence,
the descriptive title "Coriolis Balance". (Reference 2.5).
Using a polar coordinate system centered at the target vehicle and
assuming no relative gravitational acceleration, the equations of motion
are (as in Section 2.1)
Now, if the LOS acceleration, aR, equal to zero and the normal acceleration
is equal to the coriolis acceleration ( a,, = 2,6 2 ) these equations
become
p-p&'2=o
But, the second equation shows that the angular rate is constant and that the
range equation can be written as
(2.9)
/i--s2p =o $ $=a”= CONSTANT (2.10)
Equation (2.10) nOh’ shows that the coriolis balance technique also uncouples
the angular motion from the range motion. The problem is now to show that a
collision will result if this acceleration is applied. Consider the solution
to Equation (2.10) at the boundary p = 0.
36