Perturbation to Noether symmetries and adiabatic invariants for Birkhoffian systems
type: Item
instance of: scholarly article
title: Perturbation to Noether symmetries and adiabatic invariants for Birkhoffian systems
zbMATH Open document ID: 1394.70050
DOI: 10.1155/2015/790139
author: Yi Zhang
published in: Mathematical Problems in Engineering
publication date: 2018-08-27T00:00:00Z
review text: Summary: Based on El-Nabulsi dynamical model for a non-conservative system, the problem of perturbation to Noether symmetries and adiabatic invariants of a Birkhoffian system under the action of a small disturbance is proposed and studied. Firstly, the El-Nabulsi-Pfaff variational problem from extended exponentially fractional integral is presented and the El-Nabulsi-Birkhoff equations are established. Secondly, the definitions and the criterions criteria of the Noether symmetric transformations and quasisymmetric transformations of the Birkhoffian system are given, and the Noether theorems of the system are established, which reveal the inner relationship between the Noether symmetries and the conserved quantities. Thirdly, the perturbation of Noether symmetries under a small disturbance is studied, and corresponding adiabatic invariants are obtained. As special cases, the deductions in nonconservative Hamiltonian system and nonconservative Lagrangian system and standard Birkhoffian system are given. At the end of the paper, the case known as Hojman-Urrutia problem is discussed to investigate the Noether symmetries and the adiabatic invariants, the perturbation to Noether symmetries and the adiabatic invariants under El-Nabulsi dynamical model.
Mathematics Subject Classification ID: 70H09
Mathematics Subject Classification ID: 26A33
Mathematics Subject Classification ID: 37J15
zbMATH DE Number: 6927219
Wikidata QID: Q59119881
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2015/790139
OpenAlex ID: W1529109988
cites work: Q3321501
cites work: Q3996287
cites work: Q4391804
cites work: On the Birkhoffian mechanics
cites work: Fractional sequential mechanics - models with symmetric fractional derivative.
cites work: Formulation of Euler-Lagrange equations for fractional variational problems
cites work: Fractional variational calculus in terms of Riesz fractional derivatives
cites work: Variational problems with fractional derivatives: Euler–Lagrange equations
cites work: Variational problems with fractional derivatives: invariance conditions and Nöther's theorem
cites work: Fractional variational principles with delay
cites work: Necessary and sufficient conditions for the fractional calculus of variations with Caputo derivatives
cites work: Q4649595
cites work: Fractional embedding of differential operators and Lagrangian systems
cites work: Q3369889
cites work: Fractional variational problems from extended exponentially fractional integral
cites work: A periodic functional approach to the calculus of variations and the problem of time-dependent damped harmonic oscillators
cites work: Q3412087
cites work: Symmetries and conserved quantities for fractional action-like Pfaffian variational problems
cites work: Q5257772
cites work: Mathematical aspects of classical and celestial mechanics. Transl. from the Russian by E. Khukhro.
cites work: Lie symmetries, perturbation to symmetries and adiabatic invariants of Lagrange system
cites work: Q3061544
cites work: Lie symmetries, symmetrical perturbation and a new adiabatic invariant for disturbed nonholonomic systems
cites work: Perturbation to Noether symmetries and adiabatic invariants for disturbed Hamiltonian systems based on El-Nabulsi nonconservative dynamics model
cites work: FRACTIONAL QUANTUM EULER–CAUCHY EQUATION IN THE SCHRÖDINGER PICTURE, COMPLEXIFIED HARMONIC OSCILLATORS AND EMERGENCE OF COMPLEXIFIED LAGRANGIAN AND HAMILTONIAN DYNAMICS
description: scientific article; zbMATH DE number 6927219