Relativity group for noninertial frames in Hamilton's mechanics

The group epsilon(3)=SO(3)circle times T-s(3), that is the homogeneous subgroup of the Galilei group parametrized 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)circle times H-s(3), where H(3) is the Weyl-Heisenberg group that is parametrized by rates of change of position, momentum, and energy, i.e., velocity, force, and power. The group epsilon(3) is the inertial special case of the Hamilton group. (C) 2007 American Institute of Physics.