By Alexander Plakhov
Notation and Synopsis of major effects -- challenge of minimal Resistance to Translational movement of our bodies -- Newton's challenge in Media with confident Temperature -- Scattering in Billiards -- difficulties of optimum Mass Transportation -- difficulties on Optimization of suggest Resistance -- The Magnus impression and the Dynamics of a coarse Disc -- Invisible our bodies -- Retroreflectors
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Sample text
9, is called a helmet (Fig. 12); it possesses very good properties of retroreflection, yet it is not perfect. The four resulting bodies—two-dimensional retroreflectors with the corresponding hollows on their boundary—are depicted in Fig. 14. Each of the proposed shapes has its own drawbacks. The number of reflections in a tube and a notched angle is very large and goes to infinity when the reflective properties of the corresponding shape approach retroreflection. On the other hand, most particles make only one reflection in a mushroom; however, there always exists a nonzero difference between the directions of incidence and reflection.
Note in passing that the resistance of the original body C2 can be very easily decreased just by making dimples. Indeed, let the direction of v be vertical and consider a region U @C2 in the upper part of the surface @C2 whose inclination v C2 C1 Fig. 5 Spaceship. 3 Bodies Modified in a Neighborhood of Their Boundary a 31 b C2 B Fig. 6 Original spaceship C2 (a) and spaceship B with dimples (b) relative to the horizontal plane is less than 30ı . ) Then make several conical dimples in this region, with the inclination of the cone surface being exactly 30ı (Fig.
We pose the following question. Question: Given the convex bodies C1 and C2 , the spaceship velocity v, and the cloud density, what is the minimum resistance of the resulting body B? Note in passing that the resistance of the original body C2 can be very easily decreased just by making dimples. Indeed, let the direction of v be vertical and consider a region U @C2 in the upper part of the surface @C2 whose inclination v C2 C1 Fig. 5 Spaceship. 3 Bodies Modified in a Neighborhood of Their Boundary a 31 b C2 B Fig.