Some Examples of Normal Coordinates

  • Ingram Bloch


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


Normal Mode Configuration Space Rotation Matrix Equilateral Triangle Equal Mass 
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    Pain, H.J. The Physics of Vibrations and Waves. New York: Wiley, 1968.Google Scholar
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    Morse, P.M. Vibrations and Sound. 2d ed. New York: McGraw Hill, 1948.Google Scholar
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    Symon, KR. Mechanics. 3d ed. Reading MA: Addison Wesley, 1971.Google Scholar
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    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

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© Springer Science+Business Media New York 1997

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  • Ingram Bloch

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