Geodesic
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.

Voir la notice de l'article provenant de la source Math-Net.Ru

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/

[1] Hori G.-I., Publ. Astron. Soc. Japan, 18 (1966), 287

[2] Liu L., Inannen K. A., Astron. J., 90 (1985), 1906 | DOI

[3] Morbidelli A., Giogilli A., Celest. Mech., 47 (1990), 173 | DOI | MR | Zbl

[4] Sidlichovsky M., Astron. Astrophys, 259 (1992), 341

[5] Shinkin V. N., Celest. Mech., 55 (1993), 249 | DOI | MR | Zbl

[6] Shinkin V. N., Celest. Mech., 60 (1994), 307 | DOI | MR | Zbl

[7] Scholl H., Froeschle S., Astron. Astrophys., 42 (1975), 457

[8] Whittaker E. T., Watson G. N., A Course of Modern Analysis, University Press, Cambridge, 1927 | MR