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http://hdl.handle.net/10773/6322
Title: | Newton's problem of minimal resistance for bodies containing a half-space |
Author: | 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 half-space {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 cross-section 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 cross-section A, for arbitrary A. This sequence approximates the half-space; 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 half-space. © 2004 Plenum Publishing Corporation. |
Peer review: | yes |
URI: | http://hdl.handle.net/10773/6322 |
DOI: | 10.1023/B:JODS.0000024124.04032.ef |
ISSN: | 1079-2724 |
Appears in Collections: | CIDMA - Artigos |
Files in This Item:
File | Description | Size | Format | |
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2004 JDCS.pdf | 102.25 kB | Adobe PDF |
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