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Adiabatic invariants of oscillators with one degree of freedom

Adiabatic invariants of oscillators with one degree of freedom
Adiabatic invariants of oscillators with one degree of freedom
Adiabatic invariants for dynamical systems with one degree of freedom are derived. The method developed for linear dynamical systems with constant parameters is extended to systems with slowly varying parameters. The method is based on the field method concept of obtaining a conservation law from an incomplete solution of a partial differential equation. The method results in a complete set of adiabatic invariants specifying the approximate solutions for motion. A few examples, including the classical time-dependent oscillator and the Duffing oscillator with slowly varying parameters, are given to illustrate the theory.
0022-460X
695-708
Kovacic, Ivana
a84bc948-5aa9-444f-8a58-12a731808a20
Kovacic, Ivana
a84bc948-5aa9-444f-8a58-12a731808a20

Kovacic, Ivana (2006) Adiabatic invariants of oscillators with one degree of freedom. Journal of Sound and Vibration, 300 (3-5), 695-708. (doi:10.1016/j.jsv.2006.08.036).

Record type: Article

Abstract

Adiabatic invariants for dynamical systems with one degree of freedom are derived. The method developed for linear dynamical systems with constant parameters is extended to systems with slowly varying parameters. The method is based on the field method concept of obtaining a conservation law from an incomplete solution of a partial differential equation. The method results in a complete set of adiabatic invariants specifying the approximate solutions for motion. A few examples, including the classical time-dependent oscillator and the Duffing oscillator with slowly varying parameters, are given to illustrate the theory.

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Published date: 2006

Identifiers

Local EPrints ID: 43516
URI: http://eprints.soton.ac.uk/id/eprint/43516
DOI: doi:10.1016/j.jsv.2006.08.036
ISSN: 0022-460X
PURE UUID: a2eec283-9d54-4c87-ae01-27f60a58aa18

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Date deposited: 01 Feb 2007
Last modified: 15 Mar 2024 08:55

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Author: Ivana Kovacic

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