Geodesic
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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
@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/}
}
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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/