ABSTRACT
This chapter reviews the principles of the Lagrangian approach to classical mechanics whose analytical structure is described by a set on n ordinary second-order differential equations in terms of a Lagrangian function. After discussing the constraints, the principle of virtual work and D’Alembert’s principle, the Lagrangian equations of motion is derived. The chapter places special emphasis on the role of ignorable coordinates in physical systems. Apart from offering simplification of the corresponding equation of motion ignorable coordinates furnish the important result that the generalized momenta corresponding to them are constants of motion. The chapter describes Routh’s procedure of solving equations of motion when some of the coordinates are ignorable. It investigates Liouville’s class of Lagrangians and provides a method toward their solvability. The chapter provides a general treatment of the problem of small oscillations about a stable equilibrium.
