r and [alpha] are the geocentric distance and the orbital polar angle
of the mass center O, respectively.
We can calculate a new distribution function of the polar angle
by this formula.
After solving of the algebraic systems the contact pressure was calculated as a function of polar angle
for different values of the free parameters.
By following the procedure described above, we can obtain the differential elements of effective area as a function of the polar angle
Caption: Figure 3: Tangential displacement ([u.sup.*.sub.[theta]]) versus polar angle
at r = b for different wave numbers ([k.sup.(2).sub.2]b) for a tunnel in hard soil.
where [[theta].sub.A] is the polar angle
of any point A on the outer raceway.
where [[theta].sub.mi] is the polar angle
corresponding to the midpoint of the arc between adjacent polar angles
[[theta].sub.i] and [[theta].sub.i+1]; [[theta].sub.mi] [approximately equal to] ([[theta].sub.i] + [[theta].sub.i+1])/2
The amplitude [rho] of a tricomplex number is defined as [rho] = [([x.sup.3] + [y.sup.3] + [z.sup.3] - 3xyz).sup.1/3], the polar angle
[theta] of OP with respect to the trisector line (t) is given by tan [theta] = D/S, 0 [less than or equal to] [pi] and the distance from P to the origin is [d.sup.2] = [x.sup.2] + [y.sup.2] + [z.sup.2].
Depending on the location of the pixel in affine covariant region, the relation between the polar angle
of each pixel and the ellipse orientation is summarized in Table 1.
where, [[theta].sub.0] is the polar angle
of the output rays, i.e., the desired radiation direction.