Exact and adiabatic invariants of first-order Lagrange systems

Xiang Wei Chen; Mei Shang; Feng Xiang Mei

doi:10.1088/1009-1963/10/11/301

Exact and adiabatic invariants of first-order Lagrange systems

Xiang Wei Chen^*, Mei Shang, Feng Xiang Mei

^*Corresponding author for this work

School of Aerospace Engineering

Research output: Contribution to journal › Article › peer-review

10 Citations (Scopus)

Abstract

A system of first-order differential equations is expressed in the form of first-order Lagrange equations. Based on the theory of symmetries and conserved quantities of first-order Lagrange systems, the perturbation to the symmetries and adiabatic invariants of first-order Lagrange systems are discussed. Firstly, the concept of higher-order adiabatic invariants of the first-order Lagrange system is proposed. Then, conditions for the existence of the exact and adiabatic invariants are proved, and their forms are given. Finally, an example is presented to illustrate these results.

Original language	English
Pages (from-to)	997-1000
Number of pages	4
Journal	Chinese Physics
Volume	10
Issue number	11
DOIs	https://doi.org/10.1088/1009-1963/10/11/301
Publication status	Published - 2001

Keywords

Adiabatic invariant
Exact invariant
First-order Lagrange system
Symmetry

Access to Document

10.1088/1009-1963/10/11/301

Cite this

Chen, X. W., Shang, M., & Mei, F. X. (2001). Exact and adiabatic invariants of first-order Lagrange systems. Chinese Physics, 10(11), 997-1000. https://doi.org/10.1088/1009-1963/10/11/301

@article{ebc118098cb94ec4a81600b961dfb345,

title = "Exact and adiabatic invariants of first-order Lagrange systems",

abstract = "A system of first-order differential equations is expressed in the form of first-order Lagrange equations. Based on the theory of symmetries and conserved quantities of first-order Lagrange systems, the perturbation to the symmetries and adiabatic invariants of first-order Lagrange systems are discussed. Firstly, the concept of higher-order adiabatic invariants of the first-order Lagrange system is proposed. Then, conditions for the existence of the exact and adiabatic invariants are proved, and their forms are given. Finally, an example is presented to illustrate these results.",

keywords = "Adiabatic invariant, Exact invariant, First-order Lagrange system, Symmetry",

author = "Chen, {Xiang Wei} and Mei Shang and Mei, {Feng Xiang}",

year = "2001",

doi = "10.1088/1009-1963/10/11/301",

language = "English",

volume = "10",

pages = "997--1000",

journal = "Chinese Physics",

issn = "1009-1963",

publisher = "IOP Publishing Ltd.",

number = "11",

}

TY - JOUR

T1 - Exact and adiabatic invariants of first-order Lagrange systems

AU - Chen, Xiang Wei

AU - Shang, Mei

AU - Mei, Feng Xiang

PY - 2001

Y1 - 2001

N2 - A system of first-order differential equations is expressed in the form of first-order Lagrange equations. Based on the theory of symmetries and conserved quantities of first-order Lagrange systems, the perturbation to the symmetries and adiabatic invariants of first-order Lagrange systems are discussed. Firstly, the concept of higher-order adiabatic invariants of the first-order Lagrange system is proposed. Then, conditions for the existence of the exact and adiabatic invariants are proved, and their forms are given. Finally, an example is presented to illustrate these results.

AB - A system of first-order differential equations is expressed in the form of first-order Lagrange equations. Based on the theory of symmetries and conserved quantities of first-order Lagrange systems, the perturbation to the symmetries and adiabatic invariants of first-order Lagrange systems are discussed. Firstly, the concept of higher-order adiabatic invariants of the first-order Lagrange system is proposed. Then, conditions for the existence of the exact and adiabatic invariants are proved, and their forms are given. Finally, an example is presented to illustrate these results.

KW - Adiabatic invariant

KW - Exact invariant

KW - First-order Lagrange system

KW - Symmetry

UR - http://www.scopus.com/inward/record.url?scp=0035510851&partnerID=8YFLogxK

U2 - 10.1088/1009-1963/10/11/301

DO - 10.1088/1009-1963/10/11/301

M3 - Article

AN - SCOPUS:0035510851

SN - 1009-1963

VL - 10

SP - 997

EP - 1000

JO - Chinese Physics

JF - Chinese Physics

IS - 11

ER -

Exact and adiabatic invariants of first-order Lagrange systems

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this