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
The direction cosine
[lambda].sub.z'] for the local z' direction can be obtained by normalizing vector [V.sub.z'] with respect to its length.
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
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
[[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].
where [[tau].sub.xy], [[tau].sub.yz], and [[tau].sub.zx] are shear stress components under the coordinate system oxyz; [l.sub.1], [l.sub.2], and [l.sub.3], respectively, represent direction cosines
between x'-, y'-, and z'-axis and x-axis; [m.sub.1], [m.sub.2], and [m.sub.3], respectively, represent direction cosines
between x'-, y'-, and z'-axis and y-axis; and [n.sub.1], [n.sub.2], and [n.sub.3], respectively, represent direction cosines
between x'-, y'-, and z'-axis and z-axis.
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 .