Newton-Euler, Lagrange and Kirchhoff formulations of rigid body dynamics: a unified approach

TL;DR

This paper presents a unified approach to rigid body dynamics using Gauss principle, showing how Lagrange, Kirchhoff, and Newton-Euler equations emerge from different quasicoordinate choices, with discussion on group-theoretical aspects.

Contribution

It introduces a unified formulation of rigid body dynamics based on Gauss principle, linking various classical equations through quasicoordinate choices and group theory.

Findings

Unified framework for rigid body equations

Derivation of classical equations from quasicoordinates

Discussion on group-theoretical aspects of dynamics

Abstract

A unified formulation of rigid body dynamics based on Gauss principle is proposed. The Lagrange, Kirchhoff and Newton-Euler equations are seen to arise from different choices of the quasicoordinates in the velocity space. The group-theoretical aspects of the method are discussed.