Mathematical Aspects in Celestial Mechanics, the Lagrange and Euler Problems in the Lobachevsky Space

Abstract

The generalization of a test particle motion in a central field of the two immovable point-like centers to the case of a constant curvature space, in the space of Lobachevsky, is studied in the paper. The bifurcation set in the plane of integrals of motion was constructed and the classification of the domains of possible motion was carried out. The Lagrange’s problem on the pseudosphere: a mass point motion under the action of attracting center field and the analogue of a constant homogeneous field in a constant curvature space, is studied as well.