- The Countable and the Uncountable
This chapter deals with the analogy between the classical mechanics of discrete particles and that of a continuum. The reader is expected to be familiar with Lagrangian mechanics at the level of Classical Mechanics by Goldstein. Nevertheless, we provide a brief introduction to, and a derivation of Lagrange equations starting from Newton’s equations of motion. This is followed by a discussion that motivates the notion of a dynamical field as the continuum analog of a dynamical generalized coordinate (of a system with a finite number of such coordinates). The chapter also includes worked-out examples of dynamical fields encountered in everyday situations. The aim is to introduce readers to the subject through quasi-realistic examples that will enable them to formulate and solve problems.