Geometry of Routh reduction

TL;DR

This paper explores the geometric structure of Routh reduction in Lagrangian systems, revealing that the Routhian functions as a section of an affine bundle rather than a traditional function, offering new insights into reduction methods.

Contribution

It introduces a geometric perspective on Routh reduction, showing the Routhian's nature as an affine bundle section rather than a function, advancing the theoretical understanding of Lagrangian reduction.

Findings

Routhian is a section of an affine bundle, not a function

Provides a geometric interpretation of Routh reduction

Enhances understanding of Lagrangian reduction methods

Abstract

Routh reduction for Lagrangian systems with cyclic variable is presented as an example of Lagrangian reduction. It appears that Routhian, which is a generating object of reduced dynamics, is not a function any more but a section of a bundle of affine values.