Semidirect product reduction theory: a user's guide

TL;DR

This paper provides a pedagogical and rigorous exploration of the Lagrangian and Hamiltonian structures in compressible flow, illustrating the semidirect product reduction theory with concrete examples.

Contribution

It offers a clear, example-driven explanation of the semidirect product reduction theory applied to fluid dynamics, expanding on foundational works.

Findings

Clarifies the Lagrangian and Hamiltonian structures in compressible flow

Provides concrete computational examples of the reduction theory

Enhances understanding of the geometric structure of fluid dynamics

Abstract

Here we carry out computations that help clarify the Lagrangian and Hamiltonian structure of compressible flow. The intent is to be pedagogical and rigorous, providing concrete examples of the theory outlined in Holm, Marsden, and Ratiu [1998] and Marsden, Ratiu, and Weinstein [1984].