Using Bohm's quantum mechanics, a wide class of related two-parameter dynamical systems is proposed and their general properties are briefly discussed, in particular, a possibility of chaotic solutions. When the systems are reduced to a one-parameter family of equations then they are all proved to be completely integrable and integrals of the motion are found in an explicite form. The proposed class of dynamical systems can be cast into the form of Hamiltonian equations forced by a time-dependent non-Hamiltonian, periodic in time, disturbance. A systematic way of generating dynamical systems of this kind is also discussed.

PACS numbers: 05.45.+b, 03.65.--w