guidance, flight mechanics and trajectory optimization
guidance, flight mechanics and trajectory optimization
guidance, flight mechanics and trajectory optimization
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This equation gives the optimum steering schedule as a function of time.<br />
It remains to evaluate Cl <strong>and</strong> C2 from the initial condition. This objective<br />
is realized by first writing Equation (4.38) in terms of J& 8 <strong>and</strong> ~0.<br />
These values can now be used in the expression for X <strong>and</strong> Y velocity.<br />
Performing the indicated integration gives:<br />
(Recall that the coordinate system was chosen so that the initial velocity<br />
vector is along the X axis therefore ,$, = v . -<br />
0 9 j% -0 .<br />
Applying the terminal conditions reduces the y equation to:<br />
Substitutions of this in the 2 equation gives<br />
Integrating the second equation in (4.39) to get. Y(t$) <strong>and</strong> applying the<br />
boundary conditions gives<br />
(4.4oj<br />
This equation <strong>and</strong> Squation (4.40) are adequ,ate to determine the constants<br />
Cl <strong>and</strong> C2 from the initial condition. The complete solution is summarized<br />
below:<br />
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