Geodesic
Reduction in the two-body problem on the Lobatchevsky plane
Russian journal of nonlinear dynamics, Tome 2 (2006) no. 3, pp. 279-285.

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We present a reduction-of-order procedure in the problem of motion of two bodies on the Lobatchevsky plane $\mathbb H^2$. The bodies interact with a potential that depends only on the distance between the bodies (this holds for an analog of the Newtonian potential). In earlier works, this reduction procedure was used to analyze the motion of two bodies on the sphere.
Keywords: Lobatchevsky plane, first integral, reduction-of-order procedure, potential of interaction. 
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A. V. Borisov; I. S. Mamaev. Reduction in the two-body problem on the Lobatchevsky plane. Russian journal of nonlinear dynamics, Tome 2 (2006) no. 3, pp. 279-285. http://geodesic.mathdoc.fr/item/ND_2006_2_3_a1/