Motion of articulated bodies: An application of gauge invariance in classical Lagrangian mechanics

Abstract

In this paper we develop, in a very elementary way, the formulation of the Lagrangian mechanics of a system viewed from an arbitrary reference frame. In the parlance of differential geometry, this means that we formulate Lagrangian mechanics as a gauge theory. The formalism is shown to be very useful for describing the dynamics of deformable bodies in general. In particular, as we show through examples, it simplifies greatly the computation of the motion of systems of articulated rigid bodies that may be used to model diverse systems, such as trampolinists performing somersaults and twists, or direction mechanisms in satellites.