The group E(3)=SO(3) *s T(3), that is the homogeneous subgroup of the Galilei
group parameterized by rotation angles and velocities, defines the continuous
group of transformations between the frames of inertial particles in Newtonian
mechanics. We show in this paper that the continuous group of transformations
between the frames of noninertial particles following trajectories that satisfy
Hamilton's equations is given by the Hamilton group Ha(3)=SO(3) *s H(3) where
H(3) is the Weyl-Heisenberg group that is parameterized by rates of change of
position, momentum and energy, i.e. velocity, force and power. The group E(3)
is the inertial special case of the Hamilton group.Comment: Final versio