  Newtonian physics is describes macro-objects sufficiently well, however it
does not describe microobjects. A model of Extended Mechanics for Quantum
Theory is based on an axiomatic generalization of Newtonian classical laws to
arbitrary reference frames postulating the description of body dynamics by
differential equations with higher derivatives of coordinates with respect to
time but not only of second order ones and follows from Mach principle. In that
case the Lagrangian $L(t,q,\dot{q},\ddot{q},...,\dot {q}^{(n)},...)$ depends on
higher derivatives of coordinates with respect to time. The kinematic state of
a body is considered to be defined if n-th derivative of the body coordinate
with respect to time is a constant (i.e. finite). First, kinematic state of a
free body is postulated to invariable in an arbitrary reference frame. Second,
if the kinematic invariant of the reference frame is the n-th order derivative
of coordinate with respect to time, then the body dynamics is describes by a
2n-th order differential equation. For example, in a uniformly accelerated
reference frame all free particles have the same acceleration equal to the
reference frame invariant, i.e. reference frame acceleration. These bodies are
described by third-order differential equation in a uniformly accelerated
reference frame.
