Classical mechanics describes the dynamics of material bodies. The most remarkable feature of classical mechanics is the variety of approaches that can be used to solve a given problem. Equivalent formulations of mechanics include Newtonian mechanics, d’Alembert’s principle, the Lagrange equations and generalised coordinates. In principle, a given problem can be solved by any of these approaches. However, it will become clear that certain types of problems are much easier to formulate with some of these approaches than with others. For example, constrained problems (such as the motion of a bead on a wire circle) can be solved very easily using Lagrangian mechanics. This chapter presents the physical principles of Newtonian mechanics and discusses some of its main conclusions. With the introduction of d’Alembert’s principle, the Lagrange equations, which provide an alternative formulation to Newtonian mechanics, are derived step by step. They are of great practical use when dealing with systems that are restricted by certain constraints. In the Newtonian approach, these constraints have to be taken into account explicitly by introducing constraining forces in the Newtonian equations of motion, whereas in the Lagrangian formalism they can be eliminated by a clever choice of generalised coordinates, velocities and momenta. As the reader may not necessarily be familiar with the use of Lagrange’s equations, a separate section deals specifically with applications of Lagrange’s equations of the second kind. The last part of the chapter focuses on the Euler-Lagrange differential equation of the calculus of variations. It is the basis for another equivalent formulation of mechanics, the so-called Hamilton principle, which we will use in the following chapter to obtain the differential equation system of a piezoelectric bending transducer of arbitrary layer structure.