Some Examples of Normal Coordinates

  • Ingram Bloch

Abstract

In this chapter we shall apply the methods of Chapter 10 to specific physical systems. Let us take as our first example two masses, m 1 and m 2, sliding without friction on two parallel rods separated by distance D. The masses are connected by a light spring of spring constant k 0 and unstretched length S 0 < D. Letting their positions on their rods be s 1 and s 2, we use the analysis of Equations 1.10–1.15 to approximate their potential energy. Thus we have

Keywords

Normal Mode Configuration Space Rotation Matrix Equilateral Triangle Equal Mass 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Notes

  1. 1.
    French, A.P. Vibrations and Waves. New York: Norton, 1971.Google Scholar
  2. 2.
    Pain, H.J. The Physics of Vibrations and Waves. New York: Wiley, 1968.Google Scholar
  3. 3.
    Morse, P.M. Vibrations and Sound. 2d ed. New York: McGraw Hill, 1948.Google Scholar
  4. 4.
    Symon, KR. Mechanics. 3d ed. Reading MA: Addison Wesley, 1971.Google Scholar
  5. 5.
    Applications of the theory maybe found in works on molecular vibrations and on vibrations of crystal lattices, for example, in treatments of infrared and Raman spectra and of phonon spectra.Google Scholar

Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • Ingram Bloch

There are no affiliations available

Personalised recommendations