Integrable systems with linear periodic integral for the Lie algebra $\mathrm{e}(3)$

Abstract

Integrable systems with a linear periodic integral for the Lie algebra e(3) are considered. One investigates singulariries of the Liouville foliation, bifurcation diagram of the momentum mapping, transformations of Liouville tori, topology of isoenergy surfaces and other topological properties of such systems.