Lie Algebraic Structure and Poisson Conservation Law for One Class of Multi-Dimensional Coupled Oscillators

Abstract

This paper researches Lie algebraic structure and Poisson conservation law for one class of multi-dimensional coupled oscillators. The equations of motion are established, and the coupled terms in the equations of motion are eliminated by introducing normal transformations. The Lie algebraic structure and Poisson conservation law are given. Finally, an example is given to illustrate the results.