Noninertial Symmetry Group of Hamilton's Mechanics

TL;DR

This paper reveals that Hamilton's equations possess a symmetry group combining the symplectic group and a Weyl-Heisenberg group, expanding understanding of their geometric and algebraic structure beyond inertial symmetries.

Contribution

It introduces a new derivation of Hamilton's equations demonstrating their invariance under a noninertial symmetry group Sp(2n) *s H(n), which includes velocity, force, and power parameters.

Findings

Hamilton's equations have a symmetry group Sp(2n) *s H(n).

The group H(n) is parameterized by velocity, force, and power.

The inertial subgroup is the Galilei group SO(n) *s A(n).

Abstract

We present a new derivation of Hamilton's equations that shows that they have a symmetry group Sp(2n) *s H(n). Sp(2n) is the symplectic group and H(n) is mathematically a Weyl-Heisenberg group that is parameterized by velocity, force and power where power is the central element of the group. We present a new derivation of Hamilton's equations that shows that they have a symmetry group Sp(2n) *s H(n). The group Sp(2n) is the real noncompact symplectic group and H(n) is mathematically a Weyl-Heisenberg group that is parameterized by velocity, force and power where power is the central element of the group. The homogeneous Galilei group SO(n) *s A(n), where the special orthogonal group SO(n) is parameterized by rotations and the abelian group A(n)is parameterized by velocity, is the inertial subgroup.