The Inverted Pendulum as a Classical Analog of the EFT Paradigm

TL;DR

This paper models the inverted pendulum using effective field theory techniques to derive an effective Lagrangian, enabling systematic corrections and analysis of convergence behavior.

Contribution

It introduces a novel application of EFT methods to classical mechanics, specifically for analyzing the inverted pendulum with a rapidly oscillating pivot.

Findings

Derived an effective Lagrangian for the inverted pendulum

Computed corrections to the Kapitza equation systematically

Analyzed convergence of the series expansion

Abstract

The inverted pendulum is a mechanical system with a rapidly oscillating pivot point. Using techniques similar in spirit to the methodology of effective field theories, we derive an effective Lagrangian that allows for the systematic computation of corrections to the so-called Kapitza equation. The derivation of the effective potential of the system requires non-trivial matching conditions, which need to be determined order by order in the power-counting of the problem. The convergence behavior of the series is investigated on the basis of high-order results obtained by this method.