Mathematical aspects in celestial mechanics, the Lagrange and Euler problems in the Lobachevsky space. (English) Zbl 0977.70011

Vozmishcheva, Tatiana G.

Mladenov, I. M. (ed.) et al., Proceedings of the international conference on geometry, integrability and quantization, Varna, Bulgaria, September 1-10, 1999. Sofia: Coral Press Scientific Publishing. 283-298 (2000).

Let \(H^3\) be the upper sheet of the hyperboloid embedded into Minkowski space. In this paper, the author proves the integrability of Euler and Lagrange problems in the space \(H^3\). The classification of the domains of possible motion on the pseudosphere, which allows to answer the question about the trajectory equivalence of Euler and Lagrange problems in planar and curved spaces, is carried out. Additionally, the author investigates the influence of the space curvature on the integrability of the equations of motion of a point mass in a constant curvature space.
For the entire collection see [Zbl 0940.00039].

Reviewer: Mircea Crâşmăreanu (Iaşi)

MSC:

70F15	Celestial mechanics
70H06	Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics
53A35	Non-Euclidean differential geometry
51P05	Classical or axiomatic geometry and physics

Keywords:

constant curvature space; Euler problem; Lagrange problem; planar spaces; hyperboloid; Minkowski space; integrability; pseudosphere; trajectory equivalence; curved spaces; point mass