Relativity group for noninertial frames in Hamilton's 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.

Final version

References in corpus (2)

• Reciprocal relativity of noninertial frames and the quaplectic group
• Reciprocal relativity of noninertial frames: quantum mechanics

Cited by in corpus (8)

• Virtual copies of semisimple Lie algebras in enveloping algebras of semidirect products and Casimir operators
• Hamilton relativity group for noninertial states in quantum mechanics
• Noninertial Symmetry Group of Hamilton's Mechanics
• Beyond the Relativistic Point Particle: A Reciprocally Invariant System and its Generalisation
• Noninertial symmetry group with invariant Minkowski line element consistent with Heisenberg quantum commutation relations
• Projective Representations of the Inhomogeneous Hamilton Group: Noninertial Symmetry in Quantum Mechanics
• Relativity implications of the quantum phase
• Jacobi Group Symmetry of Hamilton's Mechanics