THE FLIGHT PATH

To track the flight path relative to FE, we need the velocity components in the direc­tions of the axes of Fe. These we get by transforming the velocity vector Уд into V); as shown in Appendix A.4.5

L/;z;V/І (4.4,1)

Here Leb is the matrix of direction cosines that corresponds to the reverse of the se­quence of rotations given above, which are for a transformation from FE to FB. Thus

Leb = Ьг(-ЧГ)Ц(-@)Ьх(-Ф) (4.4,2)

where Lv, Ly, Lz are respectively L„ L2, L3 of Appendix A.4. Using the rotation matrices given in Appendix A.4, and carrying out the multiplication, we get the final result (4.4,3).

sin ф sin 9 cos ф — cos ф sin ф cos ф sin 9 cos ф + sin ф sin ф

sin ф sin 9 sin ф + cos ф cos ф cos ф sin 9 sin ф — sin ф cos ф

sin Ф cos 9 cos ф cos 9

(4.4,3)

The differential equations for the coordinates of the flight path are then

-Ze-

The position of the vehicle CG is obtained by integrating the preceding equation.

“See. 5.2 of Etkin (1972).

“Appendix E of ANSI/AIAA (1992).

5Recall that the superscript signifies velocity relative to FE, and that the subscript identifies the ref­erence frame in which the components are given.