Geodesic
Defect of mapping for deformed segment of metallic mesh
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 2 (2016), pp. 5-18 Cet article a éte moissonné depuis la source Math-Net.Ru

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Metallic mesh tailoring aimed to form a parabolic reflector is identified with biunique reflection of plain’s part on a part of a paraboloid of revolution. In previous publications the authors have developed an analytical tool to assess the quality of metallic mesh tailoring for reflector antennas of any design. Its basis is a function (called the main function) the value of which depends on the ratio of first quadratic forms defining a local quadratic metric of a piece of plane and that for the corresponding segment of the metallic mesh. The integral mean of this function is called the display defect. The examples of display effect to assess the quality of metallic mesh tailoring for axisymmetric reflector are provided in previous publications. They, however, do not take into account the effect of reverse deflection of the metallic mesh between adjacent ribs of the bearing structure — the so-called mattress effect. This article fills this gap. A vector function has been built for the metallic mesh exposed to mattress effect. The functions by which the problem of display defect is solved are very complex. Polynomial approximations are constructed for them with estimated accuracy of approximation. The algorithm has been developed to calculate the display defect for practically important values for technological parameters of the axisymmetric reflector. Among these parameters are the focal parameter of the parent paraboloid, radius of the cutting out cylinder, and number of sectors.
Keywords: parabolic reflector, metallic mesh, mapping of surfaces, defect of surface-to surface mapping, deformation of metallic mesh. 
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M. S. Bukhtyak. Defect of mapping for deformed segment of metallic mesh. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 2 (2016), pp. 5-18. http://geodesic.mathdoc.fr/item/VTGU_2016_2_a0/

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