Geodesic
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.

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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://geodesic.mathdoc.fr/articles/10.1051/cocv/2019064/

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