International Journal of Mathematics and Mathematical Sciences
Volume 29 (2002), Issue 11, Pages 665-674
Breaking the symmetry of a circular system of coupled
Department of Mathematical Sciences, Virginia Commonwealth University, Richmond 23284-2014, VA, USA
Received 23 October 2000
Copyright © 2002 J. N. Boyd et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
First we compute the natural frequencies of vibration of four
identical particles coupled by ideal, massless harmonic springs.
The four particles are constrained to move on a fixed circle. The
initial computations are simplified by a transformation to
symmetry coordinates. Then the symmetry of the vibrating system
is broken by changing the mass of a single particle by a very
small amount. We observe the effect of applying the symmetry
transformation to the now slightly nonsymmetric
system. We compute the new frequencies and compare them with the
frequencies of the original symmetric system of oscillators.
Results of similar calculations for , and particles are given.