Retroreflecting Curves in Nonstandard Analysis
Retroreflecting Curves in Nonstandard Analysis
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.
FEDER/POCTI
CEOC
FCT
- University of Aveiro Portugal
Retroreflectors, Reflection, Nonstandard Analysis, Maximum resistance problems, Billiards
Retroreflectors, Reflection, Nonstandard Analysis, Maximum resistance problems, Billiards
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