Vibration of a Chain with Nonlinear Interaction
Open Access
- 1 February 1967
- journal article
- research article
- Published by Physical Society of Japan in Journal of the Physics Society Japan
- Vol. 22 (2) , 431-436
- https://doi.org/10.1143/jpsj.22.431
Abstract
Vibration of a chain of particles interacting by nonlinear force is investigated. Using a transformation exact solutions to the equation of motion are aimed at. For a special type of interaction potential of the form \begin{aligned} \phi(r){=}\frac{a}{b}e^{-br}+ar+\text{const.},\ (a,b{>}0) \end{aligned} exact solutions are actually obtained in terms of the Jacobian elliptic functions. It is shown that the system has N “normal modes”. Expansion due to vibration or “thermal expansion” of the chain is also discussed.Keywords
This publication has 4 references indexed in Scilit:
- One-Dimensional Dual TransformationProgress of Theoretical Physics Supplement, 1966
- One-Dimensional Dual TransformationJournal of the Physics Society Japan, 1965
- Computer Studies of Energy Sharing and Ergodicity for Nonlinear Oscillator SystemsJournal of Mathematical Physics, 1963
- Equipartition of Energy for Nonlinear SystemsJournal of Mathematical Physics, 1961