Geodesic
Metallic mesh tailoring for an offset reflector
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 3 (2016), pp. 5-15 Cet article a éte moissonné depuis la source Math-Net.Ru

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The term ‘tailoring’ means not only ‘cutting’ of a metallic mesh but also the method of its attachment to the supporting structures, which generally means a decrease in root-mean-square deviation (RMSD) of the reflector’s real surface from the ideal surface of the parent paraboloid. The approach of tailoring offered in this paper is based on application of SG-lines. SG-lines showed up as a solution of a (non-formal) problem to find a class of lines lying on a paraboloid of revolution and satisfying the following conditions. Locally, they should be close to geodesic lines in some reasonable sense. They can be referred to the natural parameter without significant computational problems. They should be uniquely determined by its endpoints defined on the paraboloid. These lines are used for metallic mesh tailoring for an offset reflector. An algorithm the input values of which are the design parameters of the reflector and metallic mesh has been composed. The algorithm returns a set of petals with dimensions required for tailoring. The case in which the axis of the parent paraboloid is parallel to that of the cutting cylinder is considered, as well as the case of nonparallel axes. The computational experiment carried out for specific conditions shows an error in area of 0.3653%, and the error in perimeter is of 0.0745%.
Mots-clés : paraboloid
Keywords: honeycomb panel, covering, inner energy, minimization. 
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M. S. Bukhtyak. Metallic mesh tailoring for an offset reflector. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 3 (2016), pp. 5-15. http://geodesic.mathdoc.fr/item/VTGU_2016_3_a0/

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