ABSTRACT
Symmetries can be characterized in many ways depending on the problem context. They can be continuous (translations, rotations or a boost are some of the examples) which can be obtained by successive applications of infinitesimal transformations or discrete (like space reflection or time reversal for both of which Newtonian mechanics is invariant). This chapter investigates the role of symmetry, essentially the dynamical ones, in classical mechanics. It gives a simple derivation of the condition of invariance from which the essence of Noether’s theorem which holds for a continuous class of symmetries is extracted. After working out a number of examples, the chapter discusses the problem of dynamical symmetry following an operator approach in which the notion of an evolution operator was employed. The operator method allows one to address discrete symmetries such as the parity and time-reversal operations. The chapter also briefly considers the virial theorem.
