From Newtonian Dynamics to Lagrangian Mechanics

In the first chapter, we introduce physically the Lagrangian formulation of mechanics starting from the principles of Newtonian dynamics. We define the basic notions of state of a mechanical system, constraint, and degree of freedom. We classify the possible kinds of constraints. Then we deduce the Lagrangian equations of motion using the d’Alembert principle of virtual works. We shall revisit these equations from higher standpoints in Chapters 3 and 4 after reviewing the required math tools in Chapter 2. Conservative forces are introduced, and a number of examples are discussed in detail.