Please use this identifier to cite or link to this item:
http://hdl.handle.net/10773/4153
Title: | Retroreflecting curves in nonstandard analysis |
Author: | 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. |
Peer review: | yes |
URI: | http://hdl.handle.net/10773/4153 |
ISSN: | 1812-9471 |
Appears in Collections: | CIDMA - Artigos DMat - Artigos |
Files in This Item:
File | Description | Size | Format | |
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maximumresistance.pdf | 223.52 kB | Adobe PDF | View/Open |
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