# The problem of the body of revolution of minimal resistance

Alexander Plakhov; Alena Aleksenko

ESAIM: Control, Optimisation and Calculus of Variations (2010)

- Volume: 16, Issue: 1, page 206-220
- ISSN: 1292-8119

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topPlakhov, Alexander, and Aleksenko, Alena. "The problem of the body of revolution of minimal resistance." ESAIM: Control, Optimisation and Calculus of Variations 16.1 (2010): 206-220. <http://eudml.org/doc/250701>.

@article{Plakhov2010,

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) → +∞.
},

author = {Plakhov, Alexander, Aleksenko, Alena},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Newton's problem; bodies of minimal resistance; calculus of variations; billiards},

language = {eng},

month = {1},

number = {1},

pages = {206-220},

publisher = {EDP Sciences},

title = {The problem of the body of revolution of minimal resistance},

url = {http://eudml.org/doc/250701},

volume = {16},

year = {2010},

}

TY - JOUR

AU - Plakhov, Alexander

AU - Aleksenko, Alena

TI - The problem of the body of revolution of minimal resistance

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2010/1//

PB - EDP Sciences

VL - 16

IS - 1

SP - 206

EP - 220

AB -
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) → +∞.

LA - eng

KW - Newton's problem; bodies of minimal resistance; calculus of variations; billiards

UR - http://eudml.org/doc/250701

ER -

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- A.Yu. Plakhov, Newton's problem of a body of minimal aerodynamic resistance. Dokl. Akad. Nauk390 (2003) 314–317.
- A.Yu. Plakhov, Newton's problem of the body of minimal resistance with a bounded number of collisions. Russ. Math. Surv.58 (2003) 191–192.
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