Quadratically damped oscillators with non-linear restoring force

TL;DR

This paper provides a qualitative analysis of quadratically damped oscillators with non-linear restoring forces, deriving their Hamiltonian structure and energy functions to better understand their dynamics.

Contribution

It introduces the Hamiltonian formulation and analytical energy expressions for a class of non-linear, quadratically damped oscillators, which was not previously established.

Findings

Hamiltonian structure derived for the system

Analytical form of energy functions obtained

Enhanced understanding of non-linear oscillator dynamics

Abstract

In this paper we qualitatively analyse quadratically damped oscillators with non-linear restoring force. In particular, we obtain Hamiltonian structure and analytical form of the energy functions.