Alternative perturbation approaches in classical mechanics

TL;DR

This paper compares two Lindstedt--Poincaré based perturbation methods for classical mechanics, demonstrating that one yields more accurate oscillator period calculations across all coupling constants.

Contribution

It introduces and compares two alternative perturbation techniques, highlighting the more accurate method for anharmonic oscillator period estimation.

Findings

One method is more accurate for all coupling constants.

Both methods effectively remove secular terms.

The more accurate method improves classical perturbation calculations.

Abstract

We discuss two alternative methods, based on the Lindstedt--Poincar\'{e} technique, for the removal of secular terms from the equations of perturbation theory. We calculate the period of an anharmonic oscillator by means of both approaches and show that one of them is more accurate for all values of the coupling constant.