Behaviour of the whispering gallery rays in a~vicinity of a~point where curvature of the boundary vanishes
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 11, Tome 104 (1981), pp. 146-155
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Behavior of whispering gallery rays in a vicinity of the boundary point $S=0$ with zero curvature is invertigated in two cases. In the first one boundary curvature $K$ is zero in this point, but $\frac{dK}{dS}\mid_{S=0}\ne0$. In the second one $K=\frac{dK}{dS}=0$ in the point $S=0$, but $\frac{d^2K}{dS^2}\ne0$. Results are obtained by the help of a computer and presented on the pictures.
@article{ZNSL_1981_104_a14,
author = {A. I. Lanin and M. M. Popov},
title = {Behaviour of the whispering gallery rays in a~vicinity of a~point where curvature of the boundary vanishes},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {146--155},
publisher = {mathdoc},
volume = {104},
year = {1981},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_1981_104_a14/}
}
TY - JOUR AU - A. I. Lanin AU - M. M. Popov TI - Behaviour of the whispering gallery rays in a~vicinity of a~point where curvature of the boundary vanishes JO - Zapiski Nauchnykh Seminarov POMI PY - 1981 SP - 146 EP - 155 VL - 104 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/ZNSL_1981_104_a14/ LA - ru ID - ZNSL_1981_104_a14 ER -
%0 Journal Article %A A. I. Lanin %A M. M. Popov %T Behaviour of the whispering gallery rays in a~vicinity of a~point where curvature of the boundary vanishes %J Zapiski Nauchnykh Seminarov POMI %D 1981 %P 146-155 %V 104 %I mathdoc %U http://geodesic.mathdoc.fr/item/ZNSL_1981_104_a14/ %G ru %F ZNSL_1981_104_a14
A. I. Lanin; M. M. Popov. Behaviour of the whispering gallery rays in a~vicinity of a~point where curvature of the boundary vanishes. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 11, Tome 104 (1981), pp. 146-155. http://geodesic.mathdoc.fr/item/ZNSL_1981_104_a14/