guidance, flight mechanics and trajectory optimization
guidance, flight mechanics and trajectory optimization
guidance, flight mechanics and trajectory optimization
Create successful ePaper yourself
Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.
2.4.6 N-Dimensional Lagrange Problem<br />
The concepts of Sections (2.4.1) to (2.4.5) which have been developed<br />
in connection with minimizing the integral<br />
X,9 fi<br />
J =f f(x, y, y”dy<br />
%9)1.<br />
where y is a SCalar (l-dimensiona variable, can be extended to the case<br />
in which y is an n dimensional vector<br />
(2.4.56)<br />
(2.4.58)<br />
Then, following a procedure identical to that employed in Eqs. (2.4.20) to<br />
(2.4.24) but with the scalar t( replaced by the vector y as indicated in<br />
Eq. (2.4.56), it can be shown that'RcX,y) satisfies the equation<br />
(2.4.60)<br />
where superscript T denotes the transpose <strong>and</strong> a,R <strong>and</strong> ' are the vectors<br />
du if<br />
7.5<br />
(2.4.61)
Change language