Continuous Systems

Abstract

A distinctive feature of the mechanical systems we have discussed so far is that their number of degrees of freedom is finite and hence countable. The mechanics of deformable macroscopic media goes beyond this framework. The reaction of a solid state to external forces, the flow behavior of a liquid in a force field, or the dynamics of a gas in a vessel cannot be described by means of finitely many coordinate variables. The coordinates and momenta of point mechanics are replaced by field quantities, i.e. functions or fields defined over space and time, which describe the dynamics of the system. The mechanics of continua is an important discipline of classical physics on its own and goes far beyond the scope of this book. In this epilog we introduce the important concept of dynamical field, generalize the principles of canonical mechanics to continuous systems, and illustrate them by means of some instructive examples. At the same time, this serves as a basis for electrodynamics, which is a typical and especially important field theory.