INTEGRABLE MECHANICAL SYSTEMS RELATED TO THE HARRY-DYM HIERARCHY

It is shown that all stationary and restricted flows of the Harry-Dym hierarchy have a parametrization as a set of Newton equations. They ar e new classes of integrable mechanical systems. Properties of the Harr y-Dym hierarchy are used for deriving systematically spectral-paramete r-dependent Lax representations and bi-Hamiltonian formulation for som e of these systems. They yield complete sets of integrals in involutio n which render these systems to be completely integrable.