  It is proposed how to impose a general type of ''noncommutativity'' within
classical mechanics from first principles. Formulation is performed in
completely alternative way, i.e. without any resort to fuzzy and/or star
product philosophy, which are extensively applied within noncommutative quantum
theories. Newton-Lagrange noncommutative equations of motion are formulated and
their properties are analyzed from the pure geometrical point of view. It is
argued that the dynamical quintessence of the system consists in its kinetic
energy (Riemannian metric) specifying Riemann-Levi-Civita connection and thus
the inertia geodesics of the free motion. Throughout the paper,
''noncommutativity'' is considered as an internal geometric structure of the
configuration space, which can not be ''observed'' per se. Manifestation of the
noncommutative phenomena is mediated by the interaction of the system with
noncommutative background under the consideration. The simplest model of the
interaction (minimal coupling) is proposed and it is shown that guiding affine
connection is modified by the quadratic analog of the Lorentz electromagnetic
force (contortion term).
