Shape adjustment of "FAST" active reflector

Abstract. In this paper, the relevant working principle of "FAST" Chinese Eye is studied, and a mathematical model is established to solve the equation of the ideal paraboloid. The ideal paraboloid model is obtained by rotating the paraboloid around the axis in the two-dimensional plane. On this basis, the specific solutions of each question are discussed, and the parabolic equation, the receiving ratio of the feed cabin to the reflected signal, the numbering information and coordinates of the main cable node and other parameters are obtained. This paper for solving directly above the benchmark of spherical observation of celestial bodies when ideal parabolic equation, according to the geometrical optics to knowledge should be clear all the signals of the incoming signal after the ideal parabolic will converge to the focal point of basic rules, then through converting ideal parabolic model of ideal parabolic equation in a two-dimensional plane, An optimization model was established to minimize the absolute value of the difference between the arc length and the arc length of the parabola in the diameter of 300 meters. The known conditions were substituted into Matlab to solve the equation of the ideal parabola by rotating the parabola around the axis: . In order to determine the ideal paraboloid of the celestial body, a new spatial cartesian coordinate system is first established with the line direction between the celestial body and the spherical center as the axis, so that the observed object is located directly above the new coordinate system. The same model in question 1 is established to obtain the vertex coordinates of the ideal paraboloid at this time. Then the vertex coordinates are converted to the coordinates in the original space cartesian coordinate system by rotation transformation between space cartesian coordinate systems. The solution of its vertex coordinates (-49.5287, -37.0203, -294.1763).