  Geometrical formulation of classical mechanics with forces that are not
necessarily potential-generated is presented. It is shown that a natural
geometrical "playground" for a mechanical system of point particles lacking
Lagrangian and/or Hamiltonian description is an odd dimensional line element
contact bundle. Time evolution is governed by certain canonical two-form
$\Omega$ (an analog of $dp/\dq-dH/\dt$), which is constructed purely from
forces and the metric tensor entering the kinetic energy of the system. Attempt
to "dissipative quantization" in terms of the two-form $\Omega$ is proposed.
The Feynman's path integral over histories of the system is rearranged to a
"world-sheet" functional integral. The "umbilical string" surfaces entering the
theory connect the classical trajectory of the system and the given Feynman
history. In the special case of potential-generated forces, "world-sheet"
approach precisely reduces to the standard quantum mechanics. However, a
transition probability amplitude expressed in terms of "string functional
integral" is applicable (at least academically) when a general dissipative
environment is discussed.
