The Lagrange-D'Alembert Principle in Banach Space

TL;DR

This paper extends the Lagrange-D'Alembert Principle to mechanics-like ODEs in Banach spaces, enabling analysis of geodesics in infinite-dimensional manifolds and constrained random ODEs.

Contribution

It generalizes a core principle of classical mechanics to infinite-dimensional Banach spaces, broadening its applicability.

Findings

Generalization of the Lagrange-D'Alembert Principle to Banach spaces

Application to geodesics in infinite-dimensional manifolds

Analysis of a random ODE with nonholonomic constraints

Abstract

The Lagrange-D'Alembert Principle is one of the fundamental tools of classical mechanics. We generalize this principle to mechanics-like ODE in Banach spaces. As an application we discuss geodesics in infinite dimensional manifolds and a random ODE with nonholonomic constraint.