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 Retroreflecting Curves in Nonstandard Analysis
Please use this identifier to cite or link to this item http://hdl.handle.net/10773/4153

title: Retroreflecting Curves in Nonstandard Analysis
authors: Almeida, R
Neves, V
Plakhov, A
keywords: Nonstandard Analysis
Retroreflectors
Maximum resistance problems
Reflection
Billiards
issue date: 2009
publisher: National Academy of Sciences of Ukraine
abstract: We present a direct construction of retroreflecting curves by means of Nonstandard Analysis. We construct non self-intersecting curves which are of class C(1), except for a hyper-finite set of values, such that the probability of a particle being reflected from the curve with the velocity opposite to the velocity of incidence, is infinitely close to 1. The constructed curves are of two kinds: a curve infinitely close to a straight line and a curve infinitely close to the boundary of a bounded convex set. We shall see that the latter curve is a solution of the problem: find the curve of maximum resistance infinitely close to a given curve.
URI: http://hdl.handle.net/10773/4153
ISSN: 1812-9471
source: Journal of Mathematical Physics, Analysis, Geometry
appears in collectionsCIDMA - Artigos
MAT - Artigos

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