Action-angle variables for the purely nonlinear oscillator. (November 2019)

• Record Type: Journal Article
• Authors: Ghosh, Aritra; Bhamidipati, Chandrasekhar
• Is Part Of: International journal of non-linear mechanics. Volume 116(2019)
• Page Start: 167
• Page End: 172
• Publication Date: 2019-11
• Subjects: Nonlinear oscillations -- Action-angle variables -- Ateb functions -- Generalized trigonometric functions; Nonlinear mechanics -- Periodicals; Mécanique non linéaire -- Périodiques; Nonlinear mechanics; Periodicals; 531
• DOI: 10.1016/j.ijnonlinmec.2019.06.012
• Languages: English
• ISSNs: 0020-7462

Abstract

Abstract: In this letter, we study the purely nonlinear oscillator by the method of action-angle variables of Hamiltonian systems. The frequency of the non-isochronous system is obtained, which agrees well with the previously known result. Exact analytic solutions of the system involving generalized trigonometric functions are presented. We also present arguments to show the adiabatic invariance of the action variable for a time-dependent purely nonlinear oscillator. Highlights: Action-angle variables defined for purely nonlinear oscillators. Exact solutions written in terms of generalized trigonometric function. Discussion on period function and frequency. Proposed connection between ateb and generalized trigonometric functions. Adiabatic invariance of action variable for purely nonlinear oscillator.