The Oz axis points to the mass center of the Earth E, the Ox axis is normal to the Oz axis in the orbital plane and points along the direction of an increasing polar angle
[alpha], and the coordinate system is right-hand oriented.
The distribution function of the polar angle
The temperature is sought in the form of a product of two functions, one of which depends on the variable r, and the other depends only on the polar angle
For the polar ([theta]) and azimuthal ([phi]) angles, the azimuthal angle, [phi], earns the values from 0 to 2[pi], while the polar angle
, ([theta]), earns four different values built on the source-to-detector configuration.
where r, [??], and [phi] indicates the length, polar angle
, and azimuthal angle, respectively.
This is done for the i different orientations of the polar angle
Caption: Figure 2: Radial displacement ([u.sup.*.sub.r]) versus polar angle
at r = b for different wave numbers ([k.sup.(2).sub.2]b) for a tunnel in hard soil.
[theta] is the polar angle
. C is the amplitude of a harmonic component.
where [r.sub.p] is polar radius of pole O in a polar coordinate system; [[theta].sub.p] is polar angle
of pole O in a polar coordinate system; [[sigma].sub.r] is normal stress on a microelement of the rock along the polar radius; [[sigma].sub.[theta]] is normal stress on a microelement of the rock along the polar angle
; and [[tau].sub.r[theta]] is shear stress on a microelement of the rock along the polar radius/angle.
If the interaction is within the layer, the particle's direction is updated by sampling the Henyey-Greenstein distribution for the polar angle
[theta] relative to the direction of travel.
The cam rotation angle, [fi], must be differentiated from the polar angle
[beta] that determines the position vector of point B with respect the oxy coordinate system.
We consider an infinitesimal mass dM of the sphere represented by its spherical coordinates (r, [theta], [phi]), where r is the radial distance, [theta] the polar angle
, and [phi] the azimuthal angle (see Figure 4).