guidance, flight mechanics and trajectory optimization
guidance, flight mechanics and trajectory optimization
guidance, flight mechanics and trajectory optimization
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If the matrix 121<br />
model discussed'&<br />
is taken as a function of time, then the linear gravity<br />
Section 2.1.3 can be applied. However, the matrix can be<br />
approximated by a constant for short time periods <strong>and</strong> a less than precise<br />
gravity model suitable for improving the free space model is obtained. The<br />
value of the constant matrix can be obtained as the average value of (%/ae)<br />
during the thrusting period, i.e., if K denotes the constant value which<br />
approximatess($/a,)then<br />
h<br />
fi)<br />
A?= Or<br />
&<br />
ar<br />
dt<br />
f<br />
Using this approximation, the equations of motion are<br />
0<br />
A solution to this equation is easily obtained if it is rewritten as set of<br />
two first-order equations<br />
then<br />
or<br />
where<br />
The solution for Y is<br />
y=e Af Y(O) +fkBo d+<br />
In the previous sections, only the integral term on the right h<strong>and</strong> side of the<br />
above equation was obtained. Thus, the only modification to the equations<br />
developed in those sections is the addition of the expression involving the<br />
initial conditions. Mechanization is, thus, similar.<br />
0<br />
38
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