The damped harmonic oscillator at the classical limit of the Snyder-de Sitter space

TL;DR

This paper analyzes the classical behavior of a damped harmonic oscillator within the Snyder-de Sitter space, revealing how deformation parameters influence its motion through trigonometric solutions.

Contribution

It introduces a method to solve the damped harmonic oscillator in Snyder-de Sitter space using canonical transformations compatible with deformed Poisson brackets.

Findings

Equations of motion are described by trigonometric functions.

Frequency and period depend on deformation and damping parameters.

Deformation parameters significantly influence the oscillator's motion.

Abstract

Valtancoli in his paper entitled [P. Valtancoli, Canonical transformations, and minimal length J. Math. Phys. 56, 122107 (2015)] has shown how the deformation of the canonical transformations can be made compatible with the deformed Poisson brackets. Based on this work and through an appropriate canonical transformation, we solve the problem of one dimensional (1D) damped harmonic oscillator at the classical limit of the Snyder-de Sitter (SdS) space. We show that the equations of the motion can be described by trigonometric functions with frequency and period depending on the deformed and the damped parameters. We eventually discuss the influences of these parameters on the motion of the system.