Two helpful developments towards better understanding of adiabatic invariance in classical mechanics

Abstract The topic of difficult understanding of adiabatic invariance in classical mechanics is dealt with in a more understandable way. Using the one-dimensional harmonic oscillator as an example, the goals of this paper are twofold. First, given a first-order parameter variation, the second-order...

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Main Author:	J.R. Mohallem
Format:	Article
Language:	Portuguese
Published:	Sociedade Brasileira de Física
Series:	Revista Brasileira de Ensino de Física
Subjects:	Adiabatic invariant classical mechanics
Online Access:	http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172019000200402&lng=en&tlng=en

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spelling	doaj-cb26dce54188421bb89d9709d1c97c442020-11-25T02:26:24ZporSociedade Brasileira de FísicaRevista Brasileira de Ensino de Física1806-912641210.1590/1806-9126-rbef-2018-0214S1806-11172019000200402Two helpful developments towards better understanding of adiabatic invariance in classical mechanicsJ.R. MohallemAbstract The topic of difficult understanding of adiabatic invariance in classical mechanics is dealt with in a more understandable way. Using the one-dimensional harmonic oscillator as an example, the goals of this paper are twofold. First, given a first-order parameter variation, the second-order magnitude of the correction to the adiabatic invariant is established in simple terms. Second, the identification of the action variable with the invariant quantity for slow variations of different parameters of the Hamiltonian is confirmed, by invoking the correct equation of motion in the derivation.http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172019000200402&lng=en&tlng=enAdiabatic invariantclassical mechanics
collection	DOAJ
language	Portuguese
format	Article
sources	DOAJ
author	J.R. Mohallem
spellingShingle	J.R. Mohallem Two helpful developments towards better understanding of adiabatic invariance in classical mechanics Revista Brasileira de Ensino de Física Adiabatic invariant classical mechanics
author_facet	J.R. Mohallem
author_sort	J.R. Mohallem
title	Two helpful developments towards better understanding of adiabatic invariance in classical mechanics
title_short	Two helpful developments towards better understanding of adiabatic invariance in classical mechanics
title_full	Two helpful developments towards better understanding of adiabatic invariance in classical mechanics
title_fullStr	Two helpful developments towards better understanding of adiabatic invariance in classical mechanics
title_full_unstemmed	Two helpful developments towards better understanding of adiabatic invariance in classical mechanics
title_sort	two helpful developments towards better understanding of adiabatic invariance in classical mechanics
publisher	Sociedade Brasileira de Física
series	Revista Brasileira de Ensino de Física
issn	1806-9126
description	Abstract The topic of difficult understanding of adiabatic invariance in classical mechanics is dealt with in a more understandable way. Using the one-dimensional harmonic oscillator as an example, the goals of this paper are twofold. First, given a first-order parameter variation, the second-order magnitude of the correction to the adiabatic invariant is established in simple terms. Second, the identification of the action variable with the invariant quantity for slow variations of different parameters of the Hamiltonian is confirmed, by invoking the correct equation of motion in the derivation.
topic	Adiabatic invariant classical mechanics
url	http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172019000200402&lng=en&tlng=en
work_keys_str_mv	AT jrmohallem twohelpfuldevelopmentstowardsbetterunderstandingofadiabaticinvarianceinclassicalmechanics
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Two helpful developments towards better understanding of adiabatic invariance in classical mechanics

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