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 The problem of the body of revolution of minimal resistance
Please use this identifier to cite or link to this item http://hdl.handle.net/10773/6310

title: The problem of the body of revolution of minimal resistance
authors: Plakhov, A.
Aleksenko, A.
keywords: Billiards
Bodies of minimal resistance
Calculus of variations
Newton's problem
Aerodynamic resistance
Axially symmetric
Axisymmetric bodies
Body of revolution
Calculus of variations
Convex body
Front surfaces
Resistance problems
Aerospace vehicles
Impact resistance
Bodies of revolution
issue date: 2010
abstract: Newton's problem of the body of minimal aerodynamic resistance is traditionally stated in the class of convex axially symmetric bodies with fixed length and width. We state and solve the minimal resistance problem in the wider class of axially symmetric but generally nonconvex bodies. The infimum in this problem is not attained. We construct a sequence of bodies minimizing the resistance. This sequence approximates a convex body with smooth front surface, while the surface of approximating bodies becomes more and more complicated. The shape of the resulting convex body and the value of minimal resistance are compared with the corresponding results for Newton's problem and for the problem in the intermediate class of axisymmetric bodies satisfying the single impact assumption [Comte and Lachand-Robert, J. Anal. Math. 83 (2001) 313-335]. In particular, the minimal resistance in our class is smaller than in Newton's problem; the ratio goes to 1/2 as (length)/(width of the body) → 0, and to 1/4 as (length)/(width) → +∞. © EDP Sciences, SMAI, 2008.
URI: http://hdl.handle.net/10773/6310
ISSN: 1292-8119
publisher version/DOI: http://dx.doi.org/10.1051/cocv:2008070
source: ESAIM: Control, Optimisation and Calculus of Variations
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