A One Dimensional Crystal With Nearest Neighbors Coupled Through Their Velocities

[+] Author and Article Information
J. N. Boyd, P. N. Raychowdhury

Department of Mathematical Sciences, Virginia Commonwealth University, Richmond, VA. 23284

J. Dyn. Sys., Meas., Control 103(3), 293-296 (Sep 01, 1981) (4 pages) doi:10.1115/1.3140642 History: Received January 25, 1980; Online July 21, 2009


We consider a circular array of point masses connected by springs of non-negligible mass. In the Lagrangian for the harmonic motions of this system, the movements of neighboring point masses are coupled through both the kinetic and potential energies. By use of transformations derived from the theory of projection operators, we simplify the Lagrangian and obtain the natural frequencies of the motions of the system as functions of the number of particles present. We note that for large numbers of particles, the results for our circular array will yield the frequencies of a one dimensional crystal.

Copyright © 1981 by ASME
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