Principle of Virtual Work and Lagrange’s Equations

In this chapter, we introduce the principle of virtual work, which is the foundation for all other variational principles of mechanics. We discuss d’Alembert’s principle, which is a simple application of the principle of virtual work to the dynamical equations of Newtonian mechanics, and then derive Lagrange’s equations of the 1st and 2nd kind. We shall see that the Lagrangian formulation of mechanics allows us to analyze problems that are much harder to solve when approached with a direct application of Newton’s laws.