Noether-Type First Integrals Associated with Autonomous Second-Order Lagrangians

Noether-Type First Integrals Associated with Autonomous Second-Order Lagrangians

In this paper, the analysis is centered on Noether-type first integrals in Lagrange-Hamilton dynamics based on autonomous second-order Lagrangians. More precisely, by using the classical Noether’s theorem and a non-standard Legendrian duality, the single-time and multi-time versions of Noe...

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Main Author: Savin Treanţă
Format: Article
Language:English
Published: MDPI AG 2019-08-01
Series:Symmetry
Subjects:
multi-time
conservation law
symmetry
first integral
autonomous second-order Lagrangian
Lagrange dynamics
Hamilton dynamics
Online Access:https://www.mdpi.com/2073-8994/11/9/1088
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spelling doaj-a4865acdf6014d50b93e6b3342de4dd82020-11-25T01:39:51ZengMDPI AGSymmetry2073-89942019-08-01119108810.3390/sym11091088sym11091088Noether-Type First Integrals Associated with Autonomous Second-Order LagrangiansSavin Treanţă0Department of Applied Mathematics, University Politehnica of Bucharest, 060042 Bucharest, RomaniaIn this paper, the analysis is centered on Noether-type first integrals in Lagrange-Hamilton dynamics based on autonomous second-order Lagrangians. More precisely, by using the classical Noether’s theorem and a non-standard Legendrian duality, the single-time and multi-time versions of Noether’s result are investigated for autonomous second-order Lagrangians. A correspondence is established between the invariances under flows and the first integrals for autonomous second-order Lagrangians. In this way, our results extend, unify and improve several existing theorems in the current literature.https://www.mdpi.com/2073-8994/11/9/1088multi-timeconservation lawsymmetryfirst integralautonomous second-order LagrangianLagrange dynamicsHamilton dynamics
collection DOAJ
language English
format Article
sources DOAJ
author Savin Treanţă
spellingShingle Savin Treanţă
Noether-Type First Integrals Associated with Autonomous Second-Order Lagrangians
Symmetry
multi-time
conservation law
symmetry
first integral
autonomous second-order Lagrangian
Lagrange dynamics
Hamilton dynamics
author_facet Savin Treanţă
author_sort Savin Treanţă
title Noether-Type First Integrals Associated with Autonomous Second-Order Lagrangians
title_short Noether-Type First Integrals Associated with Autonomous Second-Order Lagrangians
title_full Noether-Type First Integrals Associated with Autonomous Second-Order Lagrangians
title_fullStr Noether-Type First Integrals Associated with Autonomous Second-Order Lagrangians
title_full_unstemmed Noether-Type First Integrals Associated with Autonomous Second-Order Lagrangians
title_sort noether-type first integrals associated with autonomous second-order lagrangians
publisher MDPI AG
series Symmetry
issn 2073-8994
publishDate 2019-08-01
description In this paper, the analysis is centered on Noether-type first integrals in Lagrange-Hamilton dynamics based on autonomous second-order Lagrangians. More precisely, by using the classical Noether’s theorem and a non-standard Legendrian duality, the single-time and multi-time versions of Noether’s result are investigated for autonomous second-order Lagrangians. A correspondence is established between the invariances under flows and the first integrals for autonomous second-order Lagrangians. In this way, our results extend, unify and improve several existing theorems in the current literature.
topic multi-time
conservation law
symmetry
first integral
autonomous second-order Lagrangian
Lagrange dynamics
Hamilton dynamics
url https://www.mdpi.com/2073-8994/11/9/1088
work_keys_str_mv AT savintreanta noethertypefirstintegralsassociatedwithautonomoussecondorderlagrangians
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