VEHICLE-CARRIED VERTICAL FRAME, Fr (AXES OrYvzr)

This is a reference frame in which the origin Or is attached to the vehicle, usually at the mass center <7, and in which Ovzr is directed vertically downward, i. e. along the local g vector. The directions of the remaining axes can be specified in any convenient way. We choose Ovxv to point to the north, and Oryv east. In many applications the origin of FE is near enough to the vehicle that Earth curvature is negligible, and then Fv has axes parallel to FE, as illustrated in Fig. 4.3.

Fig. 4.3 The local (FE) and vehicle-carried (Fy) vertical reference frames.

Since Fe and Fy are both chosen so that their respective x axes point north, then Fe can be made parallel to Fr by the two consecutive rotations

(i) —ДА around 0EyE

(ii) Ay, around 0EOzEC

where ЛА = A — XE

Ay = у — yE

and (A, y) are latitude and longitude of Or

(XE, yE) are latitude and longitude of 0E.

The angular velocity of Fv relative to Fx is ыг.