Retroreflecting curves in nonstandard analysis
R. Almeidaa, V. Nevesa, A. Plakhovab
a Department of Mathematics, University of Aveiro, Campus Universitário de Santiago, 3810-193 Aveiro, Portugal
b Institute of Mathematical and Physical Sciences, University of Aberystwyth, Aberystwyth SY23 3BZ, Ceredigion, UK
We present a direct construction of retroreecting curves by means of Nonstandard Analysis. We construct non self-intersecting curves which are of class $C^1$, except for a hyper-nite set of values, such that the probability of a particle being reected from the curve with the velocity opposite to the velocity of incidence, is innitely close to 1. The constructed curves are of two kinds: a curve innitely close to a straight line and a curve innitely close to the boundary of a bounded convex set. We shall see that the latter curve is a solution of the problem: nd the curve of maximum resistance innitely close to a given curve.
Key words and phrases:
Nonstandard Analysis, retroreflectors, maximum resistance problems, reflection, billiards.
PDF file (380 kB)
MSC: 26E35, 49K30, 49Q10
R. Almeida, V. Neves, A. Plakhov, “Retroreflecting curves in nonstandard analysis”, Zh. Mat. Fiz. Anal. Geom., 5:1 (2009), 12–24
Citation in format AMSBIB
\by R.~Almeida, V.~Neves, A.~Plakhov
\paper Retroreflecting curves in nonstandard analysis
\jour Zh. Mat. Fiz. Anal. Geom.
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