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Advisor(s)
Abstract(s)
A two-dimensional body moves through a rarefied medium; the
collisions of the medium particles with the body are absolutely elastic.
The body performs both translational and slow rotational motion. It
is required to select the body, from a given class of bodies, such that
the average force of resistance of the medium to its motion is maximal.
There are presented numerical and analytical results concerning
this problem. In particular, the maximum resistance in the class of
bodies contained in a convex body K is proved to be 1.5 times resistance
of K. The maximum is attained on a sequence of bodies
with very complicated boundary. The numerical study was made for
somewhat more restricted classes of bodies. The obtained values of
resistance are slightly lower, but the boundary of obtained bodies is
much simpler, as compared to the analytical solutions.
Description
Keywords
Bodies of maximal resistance Shape optimization Billiards Numerical simulation Newton-like aerodynamic problem
Citation
Plakhov, Alexander; Gouveia, Paulo D.F. (2007). Bodies of maximal aerodynamic resistance on the plane. Cadernos de Matemática. CM07/I-12 (2007)