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New method of quantization is presented. It is based on classicalNewton-Lagrange equations of motion (representing the fundamental physical lawof mechanics) rather than on their traditional Lagrangian and/or Hamiltonianprecursors. It is shown that classical dynamics is governed by canonicaltwo-form $\Omega$, which embodies kinetic energy and forces acting within thesystem. New type of variational principle employing differential two-form$\Omega$ and ''umbilical strings'' is introduced. The Feynman path integralover histories of the system is then rearranged to ''umbilical world-sheet''functional integral in accordance with the proposed variational principle. Inthe case of potential-generated forces, world-sheet approach reduces to thestandard quantum mechanics. As an example Quantum Mechanics with friction isanalyzed in detail.Comment: 16 pages, 5 figures, comments are welcome, author is looking for  postdoctoral positio

DIRECT QUANTIZATION OF EQUATIONS OF MOTION: FROM CLASSICAL DYNAMICS TO TRANSITION AMPLITUDES VIA STRINGS