Introduction to the Differential Algebra Normal Form Algorithm using the Centrifugal Governor as an Example

TL;DR

This paper introduces the differential algebra normal form algorithm through the example of a centrifugal governor, aiming to clarify the method and promote its wider adoption in scientific research.

Contribution

It provides a detailed, step-by-step explanation of the DA normal form algorithm using a specific physical example, enhancing understanding and accessibility.

Findings

Clarified the steps of the DA normal form algorithm

Demonstrated the method on a symplectic system of the centrifugal governor

Aimed to facilitate broader use of DA normal form techniques

Abstract

This paper provides a detailed introduction into the differential algebra (DA) based normal form algorithm using the example of the symplectic one dimensional system of the centrifugal governor. The intention of this paper is to make the single steps of the algorithm as transparent as possible in the hope that the understanding and use of DA normal form methods will spread throughout the scientific community.