  A Newtonian mechanics model is essentially the model of a point body in an
inertial reference frame. How to describe extended bodies in non-inertial
(vibrational) reference frames with the random initial conditions? One of the
most general description (known as the higher derivatives formalism) consists
in taking into account the infinite number of the higher order temporal
derivatives of the coordinates in the Lagrange function. Such formalism
describes physical objects in the infinite dimensional space does not
contradict quantum mechanics and infinite dimensional Hilbert space.
