Four identical, uniformly separated particles interconnected by ideal anharmonic springs are constrained to move on a fixed, frictionless circular track. The Lagrangian for the system is written and then transformed by matrix operations suggested by the symmetry of the arrangement of springs and particles. The equations of motion derived from the transformed Lagrangian yield four natural frequencies of motion.
Boyd, J. N.; Hudepohl, R. G.; and Raychowdhury, P. N.
"Four Anharmonic Oscillators on a Circle,"
Virginia Journal of Science: Vol. 53
, Article 2.
Available at: http://digitalcommons.odu.edu/vjs/vol53/iss4/2