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Analytical Solution of Newton's Aerodynamic Problem without the Assumption of Rotational Symmetry

Lev Lokutsievskiy
Steklov Math. Inst., Moscow
Wednesday, July 3, 2019 - 14:30
The aerodynamic problem on the form of the convex body having minimal resistance while moving in rare media was proposed and solved by Sir Isaac Newton for surfaces in revolution. At the very end of the 20th century, it appears that the rejection of the hypothesis of axial symmetry allows reducing resistance: non-axially symmetric bodies with less resistance than symmetric ones of the same length and cross-section were found. The exact form of the best shape of bodies with minimal resistance was still unknown. It was considered as a challenge for experts in optimal control theory. We will present a new result, in which the body shape in the class of bodies with a vertical symmetry plane is analytically derived, and its local optimality is proved. The resistance obtained agrees well with the numerical computations performed by Lachand-Robertand, Oudet and Wachmuth, which suggests its asymptotic optimality among all convex bodies.
This is a joint work with Mikhail Zelikin (Moscow State Univ.)

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