The existence of Jacoby integral for differential equations in a finite circular Newton problem of many bodies

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.