http://arxiv.org/abs/2204.05495
Based on the background of the 2021 Higher Education Club Cup National College Students Mathematical Contest in Modeling A, according to the relevant data of the China Sky Eye (FAST) radio telescope, the main cable nodes and actuators are adjusted and controlled by mathematical modeling and computer simulation methods to realize the active reflector. The adjustment of the shape enables it to better receive the signal of the external celestial body and improve the utilization rate of the reflector, so as to achieve a higher receiving ratio of the feed cabin. In this paper, a point set mapping algorithm based on the rotation matrix of the spatial coordinate axis is proposed, that is, the mapping matrix is obtained by mathematical derivation, and the linear interpolation algorithm based on the original spherical surface and the ideal paraboloid to solve the working paraboloid is obtained. When the interpolation ratio is adjusted to 89% to satisfy the optimal solution under realistic constraints. Then, a three-dimensional spatial signal reflection model based on spatial linear invariance is proposed. Each reflective panel is used as an evaluation index. For each reflective surface, the 0-1 variable of signal accessibility on the feeder is defined. The signal is mapped to the plane where the feeder is located, which reduces a lot of computational difficulty. Finally, it is found that the panel of the feed cabin that can receive the reflected signal accounts for 19.3%. Compared with the original spherical reflection model, the working paraboloid model established in this paper has a The signal ratio has increased by 224%.
T. Shi, S. Tao and H. Wang
Wed, 13 Apr 22
58/73
Comments: 21 pages, 11 figures