Abstract:
In this paper we study the topology of a “spherical pendulum” system and construct the lattice generated by lines of integer levels of action variables for this system. We describe an algorithm for computing numerical marks of Fomenko–Zieschang invariant and monodromy matrices using these lattices. We apply this algorithm to a “spherical pendulum” system.
This publication is cited in the following 3 articles:
E. O. Kantonistova, “Topological classification of integrable Hamiltonian systems in a potential field on surfaces of revolution”, Sb. Math., 207:3 (2016), 358–399
E. O. Kantonistova, “Liouville classification of integrable Hamiltonian systems on surfaces of revolution”, Moscow University Mathematics Bulletin, 70:5 (2015), 220–222
A. T. Fomenko, E. O. Kantonistova, “Topological classification of geodesic flows on revolution $2$-surfaces with potential”, Continuous and Distributed Systems II: Theory and Applications, Studies in Systems Decision and Control, 30, ed. V. Sadovnichiy, M. Zgurovsky, Springer, 2015, 11–27