  We show that some modern geometric methods of Hamiltonian dynamics can be
directly applied to the nonholonomic Heisenberg type systems. As an example we
present characteristic Killing tensors, compatible Poisson brackets, Lax
matrices and classical $r$-matrices for the conformally Hamiltonian vector
fields obtained in a process of reduction of Hamiltonian vector fields by a
nonholonomic constraint associated with the Heisenberg system.
