Geodesic
The Jacobi problem on a plane
Russian journal of nonlinear dynamics, Tome 5 (2009) no. 1, pp. 83-86.

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3-particle systems with a particle-interaction homogeneous potential of degree $\alpha= 2$ is considered. A constructive procedure of reduction of the system by $2$ degrees of freedom is performed. The nonintegrability of the systems is shown using the Poincaré mapping.
Mots-clés : multiparticle system
Keywords: potential, Hamiltonian, reduction, integrability. 
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     title = {The {Jacobi} problem on a plane},
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A. A. Kilin. The Jacobi problem on a plane. Russian journal of nonlinear dynamics, Tome 5 (2009) no. 1, pp. 83-86. http://geodesic.mathdoc.fr/item/ND_2009_5_1_a8/