Continuous Systems, Wave Equation, Lagrangian Density, Hamilton’s Principle

Abstract

The presence of waves on periodic networks suggests that such networks may be related to continuous sys­tems such as stretched strings on which also waves can be pro­pagated. We explore this possibility by letting the segments of a periodic system become smaller and more numerous until, in the limit, the system is continuous. We concentrate our attention on the mechanical chain of masses discussed in Chapter 12, which becomes a continuous string in the limit, but shall later comment briefly on the limiting forms of other periodic systems.