When [S.sub.1] = 0, [S.sub.2] = 0, and [S.sub.3] = 0 are satisfied, Step D finally controls the single spinning angle to the target angle by the time profile of [T.sub.III], which is planned beforehand such that the position (X and Y) in the

inertial frame coincides with the target positions.

where [m.sub.c] is the mass of the aircraft, [F.sub.i] (i = x, y, z) represents the force of axes of aircraft-body coordinate frame, respectively, [bar.L], M, and N are moments of body frame, u, v, and w are speed components of body frame, [theta], [psi], and [phi] represent pitch angle, yaw angle, and bank angle, respectively, p, q, and r are angular velocity from body frame to

inertial frame resolved in body frame, [x.sub.g], [y.sub.g], and [h.sub.g] represent the position of the aircraft in

inertial frame, [I.sub.x], [I.sub.y], and [I.sub.z] are rotary inertias of axes of body frame, V is true airspeed, and [gamma], [phi] are flight-path angles between the first/second axis of wind coordinate frame and

inertial frame, respectively.

The transformation model approach proposes to align both bone volumes to the

inertial frame to give them the same location and orientation in 3D space and to allow the subsequent shape comparison.

At time t the position of the rocket in the

inertial frame are [[x.sub.0] (t) [y.sub.0] (t)]', and the angle between the i-th rope segment and the Y axis is [[theta].sub.i] (t).

They call the Cosmic frame "the

inertial frame", "flat space", "the co-moving frame", "the gravitational field" or "the most convenient frame".

It appears that I confuse light cones with

inertial frames of reference in the review at the bottom of p.

In the nomenclature chapter we denote the fixed

inertial frame of reference E as [x.sub.2][y.sub.2][z.sub.2], and the moving noninertial frame of reference B as [x.sub.1][y.sub.1][z.sub.1], which is rigidly bounded with the crane boom [BO.sub.2].

The central body frame (1) is fixed at the mass center with its final orientation reached by following the conventional aerospace sequence of three body-fixed rotations using the Euler yaw [[psi].sub.1], pitch [[theta].sub.1], and roll [[phi].sub.1] axis starting from the

inertial frame (I).

Moreover, some dynamic algorithms, which compute the acceleration due to the Earth's gravity field and the atmospheric drag, may be formulated simpler in an Earth-fixed than in an

inertial frame.

The accelerometer is fixed to

inertial frame X-Y where the acceleration is given by:

As the space station can translate and rotate freely about the

inertial frame axes, the total DOF of the system is n + 6.

Let us take n measured data by inertial measurement unit (for simplicity consider only one inertial sensor for instance gyroscope X; let us denote it by the symbol [[omega].sup.x] where [omega] represents the part of angular rate vector of the body frame with respect to the

inertial frame projected to the x axis of body frame).