Method of action-angle variables and the classical dynamics of a nonlinear Lagrangian

Abstract

The method of action-angle variables is used to obtain the complete periodic solutions of a nonlinear chiral Lagrangian system with the Lagrangian of the form L=1/2 {q² [^λ(q·q)²/(1 - ^λq²)] - [k 0q²/(1 - ^λq²)]q=(q₁, q₂, q₃) by making suitable canonical transformations. Usual semiclassical quantization procedure may then be applied to obtain the energy levels, which is shown to be in good agreement with exact results.