Kepler dynamics on a conformable Poisson manifold

TL;DR

This paper explores Kepler dynamics within a conformable Poisson manifold framework, deriving modified equations of motion, symmetry groups, and integrals of motion, thus extending classical celestial mechanics to a conformable geometric setting.

Contribution

It introduces a novel formulation of Kepler dynamics on a conformable Poisson manifold, including new Hamiltonian structures, symmetry groups, and integrals of motion.

Findings

Derived Hamiltonian vector field and modified Newton law.

Identified $SO(3), SO(4), SO(1, 3)$ symmetry groups.

Constructed recursion operators for integrals of motion.

Abstract

The problem of Kepler dynamics on a conformable Poisson manifold is addressed. The Hamiltonian function is defined and the related Hamiltonian vector field governing the dynamics is derived, which leads to a modified Newton second law. Conformable momentum and Laplace-Runge-Lenz vectors are considered, generating $SO(3), SO(4),$ and $SO(1, 3)$ dynamical symmetry groups. The corresponding first Casimir operators of $SO(4)$ and $SO(1, 3)$ are, respectively, obtained. The recursion operators are constructed and used to compute the integrals of motion in action-angle coordinates. Main relevant properties are deducted and discussed.