Vertices Of Square Research Articles

Sitnikov five-body problem with combined effects of radiation pressure and oblateness

We study the motion of negligible mass in the frame work of Sitnikov five-body problem where four equal oblate spheroids known as primaries symmetrical in all respect are placed at the vertices of square. These primaries are also considered as source of radiations moving in a circular orbit around their common center of mass. The fifth negligible mass performs oscillations along z-axis which is perpendicular to the orbital plane of motion of the primaries and passes through the center of mass of the primaries. Under the combined effects of radiation pressure and oblateness, we have developed the series solution by the Lindstedt-Poincare technique and established averaged Hamiltonians by applying the Van der Pol transformation and averaging technique of Guckenheimer and Holmes (1983). The orbits such as regular, periodic, quasi-periodic, chaotic, or stochastic have been examined with the help of Poincare surfaces of section.

Elliptic Sitnikov five-body problem under radiation pressure

We consider the square configuration of photo-gravitational elliptic restricted five-body problem and study the Sitnikov motions. The four radiating primaries are of equal mass placed at the vertices of square and the fifth body having negligible mass performs oscillations along a straight line perpendicular to the orbital plane of the primaries. The motion of the fifth body is called vertical periodic motion and the main aim of this paper is to study the effect of radiation pressure on these periodic motions in the linear approximation. Moreover, the effects of radiation pressure on the motion of fifth body have been examined with the help of Poincare surfaces of section. By escalating the radiation pressure, surrounding periodic tubes and islands disappear and chaotic motion occurs near the hyperbolic points. Further, by escalating the radiation pressure, the main stochastic region joins the escaping one.

Constant flux illumination of square cells for millimeter-wave wireless communications

The use of highly shaped-beam base-station antennas in millimeter-wave wireless communication systems may contribute to significantly enhance system performance. Previously proposed axial symmetric dielectric lenses provide a most useful constant-flux circular footprint, but they may fail to cover the regions near the vertices of square or rectangular cells, unless excessive wall illumination is allowed. This paper presents a simplified procedure to design shaped three-dimensional dielectric lenses that produce constant-flux illumination with square or rectangular footprints, suitable for indoor cells. The procedure is based on circular symmetric dielectric-lens design formulation, yet very sharp rectangular-cell boundary is obtained. Calculated and measured antenna performance is presented, not only in terms of radiation pattern, but also in terms of coverage and time-dispersion characteristic. The procedure is demonstrated for a square-cell lens and is extended for the rectangular-cell case.