Variational Methods and Periodic Solutions of Kirchhoff-type Equations. Ii

In a previous paper [1], the author and Shmel’tser started the construction of an extended Lyusternik–Shnirelman–Morse theory for the study of single-valued and multivalued functionals on the space Ω̂(M) of losed directed curves in a manifold M. The authors applied these methods to the classical problem (Kirchhoffs problem) about the free motion of a rigid body in an ideal incompressible liquid, where the fluid flows potentially and is at rest at infinity. From a modern point of view, Kirchhoff-type equations are defined by a Hamiltonian H (coinciding with the classical energy) and Poisson brackets { , } for functions in phase space (the dual space L∗ of the algebra L of the group E(3) of motions of the Euclidean space R). In the classical Kirchhoff case, we have