  It is shown that any dynamic equation on a configuration bundle $Q\to R$ of
non-relativistic time-dependent mechanics is associated with connections on the
affine jet bundle $J^1Q\to Q$ and on the tangent bundle $TQ\to Q$. As a
consequence, any non-relativistic dynamic equation can be seen as a geodesic
equation with respect to a (non-linear) connection on the tangent bundle $TQ\to
Q$. Using this fact, the relationship between relativistic and non-relativistic
equations of motion is studied. The geometric notions of reference frames and
relative accelerations in non-relativistic mechanics are introduced in the
terms of connections. The covariant form of non-relativistic dynamic equations
is written.
