Finite One-Dimensional Periodic Systems, Difference Equations

  • Ingram Bloch


In this chapter we shall discuss certain systems, mechanical and electrical, whose properties are periodic or repetitive along the length of the systems. We shall begin with systems of finite length and shall later go on to discuss infinite systems. We shall find that, in defining normal coordinates for periodic systems, we are describing wavelike motions; the study of waves in such systems will give new insights into the properties of the systems.


Normal Mode Difference Equation Standing Wave Sine Function Electrical Analog 
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  1. 1.
    A famous book on waves in periodic systems is Brillouin, L. Wave Propagation in Periodic Structures. New York: McGraw Hill, 1946; Dover Reprint, 1953.Google Scholar
  2. 2.
    Similar systems are discussed in books on lattice vibrations, for example, Seitz, F. Modern Theory of Solids. New York: McGraw Hill, 1940.Google Scholar

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© Springer Science+Business Media New York 1997

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  • Ingram Bloch

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