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.
A One Dimensional Crystal With Nearest Neighbors Coupled Through Their Velocities
- Views Icon Views
- Share Icon Share
- Search Site
Boyd, J. N., and Raychowdhury, P. N. (September 1, 1981). "A One Dimensional Crystal With Nearest Neighbors Coupled Through Their Velocities." ASME. J. Dyn. Sys., Meas., Control. September 1981; 103(3): 293–296. https://doi.org/10.1115/1.3140642
Download citation file: