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