On the straightforward perturbation theory in classical mechanics

TL;DR

This paper demonstrates that straightforward perturbation theory in classical mechanics can accurately determine period corrections despite secular term issues, making it useful for short-term analysis and educational purposes.

Contribution

It shows that simple perturbation series can provide exact period corrections and be valuable for short-term predictions in classical mechanics.

Findings

Perturbation series yield exact period corrections.

Secular terms limit long-term usefulness.

Method suitable for educational use in advanced courses.

Abstract

We show that it is possible to extract useful information from the straightforward perturbation theory in classical mechanics. Although the secular terms make the perturbation series useless for large time, these expansions yield the perturbation corrections for the period exactly and may even be useful for sufficiently short time. We think that present analysis may be suitable for an advanced undergraduate course on classical mechanics.