Geodesic
Dynamics of a~point in the~axisymmetric gravitational potential of a~massive fixed ring and center
Teoretičeskaâ i matematičeskaâ fizika, Tome 207 (2021) no. 2, pp. 319-330

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

We consider the problem of three-dimensional motion of a passively gravitating point in the potential created by a homogeneous thin fixed ring and a massive point located in the center of the ring. The motion of a passively gravitating point admits two first integrals. We first consider the integrable case of an invariant motion in the equatorial plane and then consider the general case of three-dimensional motion, where we classify the possible trajectories of a point depending on the values of the first integrals. Finally, some previous results for similar problems are compared.
Keywords: celestial mechanics, axisymmetric potential, gravitational potential, ring, first integral
Mots-clés : phase portrait, bifurcation. 
@article{TMF_2021_207_2_a10,
     author = {A. V. Sakharov},
     title = {Dynamics of a~point in the~axisymmetric gravitational potential of a~massive fixed ring and center},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {319--330},
     publisher = {mathdoc},
     volume = {207},
     number = {2},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2021_207_2_a10/}
}
TY  - JOUR
AU  - A. V. Sakharov
TI  - Dynamics of a~point in the~axisymmetric gravitational potential of a~massive fixed ring and center
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2021
SP  - 319
EP  - 330
VL  - 207
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_2021_207_2_a10/
LA  - ru
ID  - TMF_2021_207_2_a10
ER  - 
%0 Journal Article
%A A. V. Sakharov
%T Dynamics of a~point in the~axisymmetric gravitational potential of a~massive fixed ring and center
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2021
%P 319-330
%V 207
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_2021_207_2_a10/
%G ru
%F TMF_2021_207_2_a10
A. V. Sakharov. Dynamics of a~point in the~axisymmetric gravitational potential of a~massive fixed ring and center. Teoretičeskaâ i matematičeskaâ fizika, Tome 207 (2021) no. 2, pp. 319-330. http://geodesic.mathdoc.fr/item/TMF_2021_207_2_a10/