| Abstract: | A cyclic chain of n equal classic particles coupled by anharmonic forces has a set of extended vibrational modes, for which exact solutions are given. This requires for the power law of the forces certain conditions to be fulfilled. Each mode is characterized by a wave number and the undulations of the particles depend on the total energy and on a new constant of motion that formally expresses a kind of angular momentum. Exact solutions for n = 7 with a twelfth power potential are discussed. |
