The integrable cases of the three-body problem at third-order resonance under the oblateness of the central planet
Fundamentalʹnaâ i prikladnaâ matematika, Tome 1 (1995) no. 4, pp. 1045-1058
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In the present paper the general spatial and restricted elliptic spatial three-body problem at third-order resonance $j:(j+3)$ are analytically integrated by quadratures with the help of the Weierstrass functions, using an expansion of the disturbing function up to and including the third-degree terms in the eccentricities and in the inclinations.
@article{FPM_1995_1_4_a13,
author = {V. N. Shinkin},
title = {The integrable cases of the three-body problem at third-order resonance under the oblateness of the central planet},
journal = {Fundamentalʹna\^a i prikladna\^a matematika},
pages = {1045--1058},
publisher = {mathdoc},
volume = {1},
number = {4},
year = {1995},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/FPM_1995_1_4_a13/}
}
TY - JOUR AU - V. N. Shinkin TI - The integrable cases of the three-body problem at third-order resonance under the oblateness of the central planet JO - Fundamentalʹnaâ i prikladnaâ matematika PY - 1995 SP - 1045 EP - 1058 VL - 1 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/FPM_1995_1_4_a13/ LA - ru ID - FPM_1995_1_4_a13 ER -
%0 Journal Article %A V. N. Shinkin %T The integrable cases of the three-body problem at third-order resonance under the oblateness of the central planet %J Fundamentalʹnaâ i prikladnaâ matematika %D 1995 %P 1045-1058 %V 1 %N 4 %I mathdoc %U http://geodesic.mathdoc.fr/item/FPM_1995_1_4_a13/ %G ru %F FPM_1995_1_4_a13
V. N. Shinkin. The integrable cases of the three-body problem at third-order resonance under the oblateness of the central planet. Fundamentalʹnaâ i prikladnaâ matematika, Tome 1 (1995) no. 4, pp. 1045-1058. http://geodesic.mathdoc.fr/item/FPM_1995_1_4_a13/