where [u.sub.1], [u.sub.2], and [u.sub.3] are, respectively, the direction cosines of the attitude angels of the platform, and T(t), L(t), and V(t) are, respectively, the transverse, longitudinal, and vertical components of Earth's total magnetic field measured by the vector magnetometer.
where [c.sub.i], i = 1, ..., 3, denotes the compensation coefficients of the permanent magnetic fields and [A.sub.i], i = 1, ..., 3, denotes the variables constituted by the direction cosines.
Additionally, this method can provide automatically paired 2D direction cosine
estimates without matching pair and deal with the correlated signals directly.
The half-symmetric Legendre-Chebyshev quadrature sets ([R.sub.n][T.sub.n]) are offered for users, whose set of direction cosines
along [xi] axis is different from the sets along other two axes .
So the direction cosines
[[lambda].sub.x'], [[lambda].sub.yx'], and [[lambda].sub.z'] of the local coordinate system established at different Gauss point with respect to the global coordinate system are different with each other.
[a.sub.ij] o[x.sub.o] o[x.sub.b] [a.sub.11] = cos [psi] x cos [theta] o[y.sub.b] [a.sub.21] = sin [theta] o[z.sub.b] [a.sub.31] = -sin [psi] x cos [theta] [a.sub.ij] o[y.sub.o] o[x.sub.b] [a.sub.12] = sin[psi] x sin[psi] x cos[phi] x cos[psi] x sin[phi] x sin[theta] o[y.sub.b] [a.sub.22] = cos[phi] x cos[theta] o[z.sub.b] [a.sub.32] = cos[psi] x sin[phi] x sin[psi] x cos[phi] x sin[theta] [a.sub.ij] o[z.sub.o] o[x.sub.b] [a.sub.13] = sin[psi] x cos[phi] + cos[psi] x sin[psi] x sin[theta] o[y.sub.b] [a.sub.23] = -sin[phi] x cos[theta] o[z.sub.b] [a.sub.33] = cos[psi] x cos[phi] - sin[psi] x sin[phi] x sin[theta]
If the direction cosines
are positive, the directional radiance is known on the faces W and S and they are unknown on the faces E and N of the (i, j)-cell and also in the centre P.
The main idea of the method uses MUSIC-based procedure to search the true direction cosine
estimate from a set of ambiguous candidate estimates.
However, both objects are having deferent type direction cosines
(Dcs) and direction ratios (Drs).
Principal components, standard deviation of major and minor axis, direction cosines
, and eccentricity of the pattern were derived for each storm.
In space analytic geometry, another new coordinate system can be generated through the initial coordinate system which is rotated one or more times relative to the third coordinate system, and the relationship between the new and old coordinate system can be described with direction cosine
. According to this theory, the triaxial acceleration is regarded as a vector, whose three direction cosines
are the cosines of three angles between the vector and the three axes, and then the coordinate transformation from the smartphone's coordinate system to the inertial coordinate system will be realized.
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.