On the Formulation of Lagrange's Equations with Respect to Moving Coordinate Systems: Application to a Point Mass Vibrating on a Rotating Base

Abstract

Lagrange's equations are a well known tool for establishing equations of motion of discrete systems. Kinetic energy, which plays a central role in their use, has to be formulated with respect to an inertial system. Lagrange's equations can be formulated favorably with respect to a moving coordinate system as well (e.g. for mechanical systems which themselves are on a moving base), in that the relative kinetic energy is employed. This enables one to get better insight into various inertia forces. The theory revisited is applied to a point mass vibrating on a rotating base.