Topological invariants of pseudo-Euclidean Zhukovsky integrable case

E. S. Agureeva^ab, V. A. Kibkalo^ab, V. A. Chertopolokhov<sup>cb

a</sup> Moscow Center for Fundamental and Applied Mathematics (Moscow)
^b Lomonosov Moscow State University (Moscow)
^c Supersonic center (Moscow)

Abstract: We study the pseudo-Euclidean analogue of the integrable Zhukovsky case for an axisymmetric body. Two essential parameters were found on the multidimensional parameter space, and the separating set was constructed. The bifurcation curve arrangement on the momentum map plane is explicitly described depending on parameter values. Fomenko invariants analogs for non-singular isoenergy and isointegral surfaces are computed. A visualization of the output of the algorithm for constructing labeled graphs for non-singular isoenergetic surfaces is given.

Keywords: Integrable system, rigid body dynamics, Liouville foliation, pseudo-Euclidean space, Zhukovsky case, topological invariant, singularity.

UDC: 517.938.5

Received: 30.04.2025
Accepted: 17.10.2025

DOI: 10.22405/2226-8383-2025-26-4-223-238