Then, the
direction cosine and direction sine between normal unit vectors and x- and y-axes are as follows:
where [u.sup.(k)] is the position vector of any point on the mid-plane of the kth layer, [B.sup.(k)] is the
direction cosine transformation matrix from floating coordinate system (O, e) of the kth layer (shown in Figure 3) to inertial reference coordinate system ([O.sub.0], [e.sup.(0)]), and
So we obtain [[??].sup.a.sub.tp] = exp(j[[omega].sup.a.sub.tp]), [[??].sup.a.sub.rp] = exp(j[[omega].sup.a.sub.rp]), and the set of low-variance but cyclically ambiguous
direction cosine estimates
In this paper, we discuss segmentation method uses three angles [alpha], [beta], [gamma] to control the surface area, boundary angle through (Cos[alpha], Cos[beta], and Cos[gamma]) and Boundary
Direction Cosine (BDC).
[[mu].sub.j] =
direction cosine in j discrete directions
where [u.sub.k] = sin [[theta].sub.k] cos [[phi].sub.k] and [v.sub.k] = sin [[theta].sub.k] sin [[phi].sub.k] are
direction cosines mapping with azimuth and elevation angles and [g.sub.k] is the gain of the kth incident signal.
Relation between
Direction cosine and direction ration
where [Mathematical Expression Omitted] is the
direction cosine of the axis [u.sub.m] of the structural unit with respect to the axis [x.sub.i] of the bulk specimen [ILLUSTRATION FOR FIGURE A-1 OMITTED].
The
direction cosines of the attitude angels of the platform are calculated by the output of the vector magnetometer as follows:
From the point of view to satisfy more moment conditions for integration accuracy, the even-odd moment quadrature sets (E[O.sub.N]) have the ability to accurately integrate not only even moments but also odd moments of
direction cosines in one octant [12].