Author(s):  V.I. Vanko, Prof., Bauman Moscow State Technical University, Moscow, Russia, vvanko@mail.ru

Issue:  Volume 51, № 2

Rubric:  Mathematics

Annotation:  This article is devoted to two anniversaries taking place in 2008: 375 and 155 the day of birth of Isaak Newton and from the day of birth of academician A.N. Krylov. A. Krylov (prominent shipbuilder and applied mathematician) in Russian translated a book “The mathematical principles of natural philosophy” the first in Russian language and made clear the comments “dark’ places ot text. After a book became accessiable to the native researchers. The drag’s low (proportionally to square motion’s velocity) is concluded; the formula of resistance force to moving body is obtained; the overall dimensions of the least drag’s straight truncated cone is determined; the boundary conditions are discussed; the presence platform bow’s is based. The variational task about the rotational body with the least drag is formulated and solved. The outstanding role of academician A. Krylov in the modern variational solution problem is emphasized. The author’s results are presented: an algebraic investigation of existence and uniquiness the Newton’s problem solution; example of the bow section’s design of the least drag. The sufficient condition solution uniquiness’ as a limitation for the dimensions of bow is received. The native scientists contribution to the development of the optimal forms vehicles is marked: the problem about minimization wave resistance for flying apparatus is solved.

Keywords:  drag, minimization, revolution body, Newton’s problem, existence and uniqueness of solution

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