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title:  Newton's problem of minimal resistance for bodies containing a halfspace 
authors:  Plakhov, A. 
keywords:  Billiards Body of minimal resistance Multiple collisions Newton's problem Integral equations Set theory Theorem proving Vectors Velocity Minimal resistance Multiple collisions Newton problem Unbounded bodies Bodies of revolution 
issue date:  2004 
abstract:  We consider Newton's problem of minimal resistance for unbounded bodies in Euclidean space ℝd, d ≥ 2. A homogeneous flow of noninteracting particles of velocity v falls onto an immovable body containing a halfspace {x : (x, n) < 0} ⊂ ℝd, (v, n) < 0. No restriction is imposed on the number of (elastic) collisions of the particles with the body. For any Borel ser A ⊂ {v}⊥ of finite measure, consider the flow of crosssection A: the part of initial flow that consists of particles passing through A. We construct a sequence of bodies that minimize resistance to the flow of crosssection A, for arbitrary A. This sequence approximates the halfspace; any particle collides with any body of the sequence at most twice. The infimum of resistance is always one half of corresponding resistance of the halfspace. © 2004 Plenum Publishing Corporation. 
URI:  http://hdl.handle.net/10773/6322 
ISSN:  10792724 
publisher version/DOI:  http://dx.doi.org/10.1023/B:JODS.0000024124.04032.ef 
source:  Journal of Dynamical and Control Systems 
appears in collections  CIDMA  Artigos

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