Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 11, Tome 104 (1981), pp. 146-155
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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/
@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},
year = {1981},
volume = {104},
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
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
%U http://geodesic.mathdoc.fr/item/ZNSL_1981_104_a14/
%G ru
%F ZNSL_1981_104_a14
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.
