Analysis on the Foucault pendulum by De Alembert Principle and Numerical Simulation

TL;DR

This paper introduces a novel method based on De Alembert Principle for analyzing Foucault pendulum motion, avoiding small-angle approximations, and demonstrates its effectiveness through numerical simulations revealing complex non-linear behaviors.

Contribution

The paper presents a new approach using De Alembert Principle to derive motion equations for the Foucault pendulum without small-angle assumptions, enhancing accuracy.

Findings

Revealed non-linear features of pendulum motion through numerical analysis.

Compared new method with traditional approaches, showing its advantages.

Observed near-harmonic argument changes and pulsing swing plane behavior.

Abstract

In this paper, we handle the problem of the motion of the Foucault pendulum. We explore a new method induced from the De Alembert Principle giving the motional equations without small-amplitude oscillation approximation. The result of the problem is illustrated by numerical analysis showing the non-linear features and then with a comparison with a common method, showing the merit of this new original method. The result also shows that the argument changes in near-harmonic mode and the swing plane changes in pulsing way.