Abstract
It is proposed how to impose a general type of noncommutativity within classi- cal 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 iner- tia 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 con- nection is modified by the quadratic analog of the Lorentz electromagnetic force (contortion term).
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