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.