Geodesic
Studying the stability of equilibrium solutions in the elliptic restricted many-body problem with the computer algebra methods
Matematičeskoe modelirovanie, Tome 18 (2006) no. 10, pp. 102-112

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

Stability of equilibrium solutions in the elliptic restricted many-body problem of Sitnikov's kind is studied. Equations of the disturbed motion are obtained in the form of the Hamiltonian system of differential equations with periodic coefficients. We have found the domains of instability of the system in the parameter space and shown that it is stable in Lyapunov sense if an eccentricity of the bodies orbits is sufficiently small. It has been proved that for small values of the eccentricity nonlinear terms in the equations of motion do not disturb stability of the system even if the fourth order resonance takes place. All calculations are done with the computer algebra system Mathematica. 
@article{MM_2006_18_10_a9,
     author = {A. N. Prokopenya},
     title = {Studying the stability of equilibrium solutions in the elliptic restricted many-body problem with the computer algebra methods},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {102--112},
     publisher = {mathdoc},
     volume = {18},
     number = {10},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2006_18_10_a9/}
}
TY  - JOUR
AU  - A. N. Prokopenya
TI  - Studying the stability of equilibrium solutions in the elliptic restricted many-body problem with the computer algebra methods
JO  - Matematičeskoe modelirovanie
PY  - 2006
SP  - 102
EP  - 112
VL  - 18
IS  - 10
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2006_18_10_a9/
LA  - ru
ID  - MM_2006_18_10_a9
ER  - 
%0 Journal Article
%A A. N. Prokopenya
%T Studying the stability of equilibrium solutions in the elliptic restricted many-body problem with the computer algebra methods
%J Matematičeskoe modelirovanie
%D 2006
%P 102-112
%V 18
%N 10
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2006_18_10_a9/
%G ru
%F MM_2006_18_10_a9
A. N. Prokopenya. Studying the stability of equilibrium solutions in the elliptic restricted many-body problem with the computer algebra methods. Matematičeskoe modelirovanie, Tome 18 (2006) no. 10, pp. 102-112. http://geodesic.mathdoc.fr/item/MM_2006_18_10_a9/