Principle of Virtual Work, Lagrange’s Equation and Hamilton’s Principle

Abstract

This chapter presents several of the most important concepts from analytical dynamics. The most important of these concepts to us is Lagrange’s equation and how it can be used for the derivation of governing equations of motion. The equation is especially useful for the derivation of the equations of motion for systems, discrete or continuous, with more than one degree of freedom, where the Newtonian free body diagrams become more difficult to apply. We will also derive Hamilton’s principle, an integral energy formulation, also applicable to both discrete and continuous systems, and see how it is connected to Lagrange’s equation.