**Abstract: **
Classical Newton-Lagrange equations of motion represent the
fundamental
physical law of mechanics. Their traditional Lagrangian and/or
Hamiltonian
precursors when available are essential in the context of
quantization.
However, there are situations which lack usual Lagrangian and/or
Hamiltonian
settings.
Seminar will discuss classical and quantal descriptions
of such systems by
introducing a certain canonical two-form $\Omega$ in
the extended velocity
(or phase) space. By construction $\Omega$ embodies kinetic energy
(metric
which specifies inertia properties) and forces acting within the
system (not their
potential!). New type of variational principle will be presented and
the Feynman
path quantization will be rearranged into a surface functional
integration. In the
case of potential-generated forces, the proposed approach will reduce
to the
standard quantum mechanics.