Study on the mechanical system related to Hahn's discrete time derivative

TL;DR

This paper develops a deformed classical mechanics framework using Hahn's discrete time derivative, exploring motion dynamics and extending to resistive media through quantum variational calculus.

Contribution

It introduces a novel deformed mechanics model based on Hahn's calculus and extends classical motion equations to include resistance effects using quantum variational calculus.

Findings

Deformed equations for constant velocity and acceleration motion.

Extension to motion in resisting media with proportional retarding force.

Use of ($q,w$)-series identities in mechanics.

Abstract

In this paper, we use the quantum variational calculus related to Hahn's discrete time derivative construct the deformed version for the classical mechanics related to the Hahn's calculus. We deal with the deformed dynamics such as the motion with constant velocity and the motion with constant acceleration. Moreover, we extend our work to the motion of a body in a resisting medium by using the new identity for an infinite ($q,w$)-series, where the retarding force is assumed to be proportional to the deformed average velocity.