Relativity group for noninertial frames in Hamilton's mechanics

TL;DR

This paper extends the concept of transformation groups in mechanics from inertial frames to noninertial frames within Hamiltonian mechanics, introducing the Hamilton group as the relevant symmetry group.

Contribution

It identifies the Hamilton group Ha(3) as the continuous transformation group for noninertial frames in Hamiltonian mechanics, generalizing the inertial case E(3).

Findings

The Hamilton group Ha(3) includes rotations and transformations related to velocities, forces, and power.

E(3) is a special case of Ha(3) for inertial frames.

The work provides a group-theoretic framework for noninertial transformations in Hamiltonian mechanics.

Abstract

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.