meridional plane

meridional plane

[mə′rid·ē·ən·əl ′plān]
(optics)
A plane containing the axis of an optical system. Also known as tangential plane.
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Despite tire fact that early papers on this topic studied only regular orbits in terms the meridional plane (Martinet & Mayer, 1975, Manabe, 1979, Greiner, 1987, Lees & Schwarzschild, 1992), soon after, the existence of chaos on the orbital motion started to be considered by Caranicolas (1996) and Caranicolas & Papadopoulos (2003).
where [f.sub.m] = -[R.sub.i] cos ([A.sub.i])/2 is the focal length in meridional plane (x-z plane) and [f.sub.s] = -[R.sub.i]/2 cos([A.sub.i]) is the focal length in the sagittal plane (y-z plane).
T([L.sub.j]) is 5 x 5 ray transfer matrix for free space propagation in a homogeneous medium and R([[phi].sub.j]) is the coordinate rotation matrix when considering the change of each reflective meridional plane, where [[phi].sub.j] is the meridional plane rotation angle relative to the last meridional plane.
However, the reflection plane (meridional plane, namely, [T.sub.ix]-0-[T.sub.iz] plane) for each reflection in the UMS varied each time, and the [T.sub.ix]-0-[T.sub.iz] plane is fixed as a precondition in the derivation based on Figure 5.
Sampling points [P.sub.i] are selected along the circle for the radius of r, with the same angular interval ps in the range of 0[degrees] [less than or equal to] [theta] [less than or equal to] 90[degrees], both on the azimuth plane ([psi] = 0[degrees]) and the meridional plane ([psi] = 90[degrees]).
[[theta]'.sub.ms0] and [[theta]'.sub.ms90] are the subtended angle of the reflector in the azimuth plane and meridional plane, respectively.
The more consistent the feed radiation patterns in the azimuth plane and meridional plane are, the better far-field response of the reflector IRA is [27].
Note that the orbit of particle is confined to the plane defined by the effective potential, known as meridional plane. The numerical integration is performed through the Runge-Kutta method of fourth order and by checking that energy is conserved within a tolerance of [10.sup.-10].
In figure 3 we display the meridional plane with the with initial conditions z = 0, R = 0.78, [V.sub.R] = 0, and the same parameters considered above.
orbits in the meridional plane with initial conditions z = 0, R = 0.78, [V.sub.R] = 0 and the same parameters considered above.
5), an asymmetric power pattern in the meridional plane with an up-shift of 15[degrees] (Fig.
where x = {A, B, C, D, E, F, w, w1, a3, a4, h7, t2}, mld(x) is the main lobe direction of the power pattern in the meridional plane for x.