The analytical solution of Newton’s aerodynamic problem in the class of bodies with vertical plane of symmetry and developable side boundary
ESAIM: Control, Optimisation and Calculus of Variations, Tome 26 (2020), article no. 15.

The method of Hessian measures is used to find the differential equation that defines the optimal shape of nonrotationally symmetric bodies with minimal resistance moving in a rare medium. The synthesis of optimal solutions is described. A theorem on the optimality of the obtained solutions is proved.

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DOI : 10.1051/cocv/2019064
Classification : 49N99 
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Lokutsievskiy, L.V.; Zelikin, M.I. The analytical solution of Newton’s aerodynamic problem in the class of bodies with vertical plane of symmetry and developable side boundary. ESAIM: Control, Optimisation and Calculus of Variations, Tome 26 (2020), article no. 15. doi : 10.1051/cocv/2019064. http://www.numdam.org/articles/10.1051/cocv/2019064/

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This work is financially supported by RFBR grant 20-01-00469.