Some multidimensional integrable cases of nonholonomic rigid body dynamics

In this paper we study the dynamics of the constrained $n$--dimensional rigid body (the Suslov problem). We give a review of known integrable cases in three dimensions and present their higher dimensional generalizations.Comment: 10 page

Noncommutative integrability and action-angle variables in contact geometry

We introduce a notion of the noncommutative integrability within a framework of contact geometry.Comment: 22 pages,1 figure, Theorem 5 slightly modifie

Noether symmetries and integrability in time-dependent Hamiltonian mechanics

We consider Noether symmetries within Hamiltonian setting as transformations that preserve Poincar\'e-Cartan form, i.e., as symmetries of characteristic line bundles of nondegenerate 1-forms. In the case when the Poincar\'e-Cartan form is contact, the explicit expression for the symmetries in the inverse Noether theorem is given. As examples, we consider natural mechanical systems, in particular the Kepler problem. Finally, we prove a variant of the theorem on complete (non-commutative) integrability in terms of Noether symmetries of time-dependent Hamiltonian systems.Comment: 18 pages, 2 figures, to appear in Theoretical and Applied Mechanic