Matematičeskoe modelirovanie, Tome 10 (1998) no. 6, pp. 118-122
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E. A. Grebenikov. The existence of Jacoby integral for differential equations in a finite circular Newton problem of many bodies. Matematičeskoe modelirovanie, Tome 10 (1998) no. 6, pp. 118-122. http://geodesic.mathdoc.fr/item/MM_1998_10_6_a9/
@article{MM_1998_10_6_a9,
author = {E. A. Grebenikov},
title = {The existence of {Jacoby} integral for differential equations in a~finite circular {Newton} problem of many bodies},
journal = {Matemati\v{c}eskoe modelirovanie},
pages = {118--122},
year = {1998},
volume = {10},
number = {6},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MM_1998_10_6_a9/}
}
TY - JOUR
AU - E. A. Grebenikov
TI - The existence of Jacoby integral for differential equations in a finite circular Newton problem of many bodies
JO - Matematičeskoe modelirovanie
PY - 1998
SP - 118
EP - 122
VL - 10
IS - 6
UR - http://geodesic.mathdoc.fr/item/MM_1998_10_6_a9/
LA - ru
ID - MM_1998_10_6_a9
ER -
%0 Journal Article
%A E. A. Grebenikov
%T The existence of Jacoby integral for differential equations in a finite circular Newton problem of many bodies
%J Matematičeskoe modelirovanie
%D 1998
%P 118-122
%V 10
%N 6
%U http://geodesic.mathdoc.fr/item/MM_1998_10_6_a9/
%G ru
%F MM_1998_10_6_a9
Existence of Jacoby integral is proved in a finite circular problem of $n+1$ bodies ($n\geq3$). In this dynamic model $n$ bodies $P_0,P_1,\dots,P_{n-1}$ with masses $m_0,m_1,\dots,m_{n-1}$ and point $P$ (with mass $m=0$) mutually pull one another under the law of Newton and $n$ massive bodies move on circular orbits around the common centre of mass $G$, whereas $(n+1)$s body $P$ move in three-dimensional space under action gravitation forces.
