| Virginia
Journal of Science.
2002. Vol 53 (4) : 191-198 |
| Four
Anharmonic Oscillators on a Circle J. N. Boyd, R.G. Hudepohl and P.N. Raychowdhury, Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, Richmond, VA 23284-2014 U.S.A. ABSTRACT
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. |