A conformal invariance for generalized Birkhoff equations

Feng-Xiang, Mei; Jia-Fang, Xie; Tie-Qiang, Gang

doi:10.1007/s10409-008-0176-8

Cited by 26 publications

(18 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In 1997, Galiullin et al [18] discussed the conformal invariance of Birkhoff system and deduced Nother conserved quantities from conformal invariance. Mei et al [19] extend the conformal invariance to generalized Birkhoff equations and gave the Noether conserved quantities. The key question to the conformal invariance of dynamics is to find out the conformal factor.…”

Section: Introductionmentioning

confidence: 99%

Conformal invariance of Mei symmetry and conserved quantities of Lagrange equation of thin elastic rod

Wang

Xue

2015

Nonlinear Dyn

View full text Add to dashboard Cite

By Kirchhoff dynamic analogy, the thin elastic rod static equals to rotation of rigid body dynamic. The analytical mechanics methods reflect their advantages in the study of the modeling and equilibrium and stability of elastic rod static, especially for the constrained problems. The Lagrangian structure of the equation of motion for elastic rod is deduced from the integral variational principle. The definition of conformal invariance of Mei symmetry of elastic rod in Lagrangian form is given. The determining equation of conformal invariance of Mei symmetry is obtained based on the Lie point transformation group. The relation between conformal invariance of Mei symmetry and Mei symmetry is discussed. The structure equation and conserved quantity by using the Lagrangian structure along arc coordinate deduced from conformal invariance of Mei symmetry of elastic rod are constructed. Take rod with circular cross section as example to illustrate the application of the results get in this paper. These conserved quantities will be helpful in the study of exact solutions and stability, as well as the numerical simulation of the thin elastic rod nonlinear mechanics.

show abstract

Section: Introductionmentioning

confidence: 99%

Conformal invariance of Mei symmetry and conserved quantities of Lagrange equation of thin elastic rod

Wang

Xue

2015

Nonlinear Dyn

View full text Add to dashboard Cite

show abstract

“…In 1997, Galiullin et al [19] discussed the conformal invariance of Birkhoff system and deduced Noether conserved quantities from conformal invariance. Mei et al [20] extended the conformal invariance to generalized Birkhoff equations and gave the Noether conserved quantities. The key question to the conformal invariance of dynamics is to find out the conformal factor.…”

Section: Introductionmentioning

confidence: 99%

Conformal Invariance and Conserved Quantities for Lagrange Equation of Thin Elastic Rod

Wang

Feng

2017

Acta Phys. Pol. A

View full text Add to dashboard Cite

Basing on the analytical mechanics methods, the Lagrangian equations of thin elastic rod is constructed. The definition of conformal invariance for the Lagrange mechanics of elastic rod is given. The criterions that conformal invariance of elastic rod is the Lie symmetry are obtained based on the Lie point transformation group. The structure equation and conserved quantity deduced from conformal invariance of elastic rod are constructed. Take twist rod as an example to illustrate the application of the results got in this paper.

show abstract

“…We have discussed the conformal invariance and conserved quantities of Lie symmetry for Lagrange systems, Hamilton systems, general holonomic systems and nonholonomic systems [25][26][27][28], The authors of Refs. [29][30][31][32][33] have studied the conformal invariance of Lie symmetry for first-order differential equations, generalized Birkhoff equations, variable mass systems, general holonomic systems in phase space and Birkhoffian systems in event space, and so on. In Refs.…”

Section: Introductionmentioning

confidence: 99%

Conformal Invariance and Conserved Quantity of the Higher-Order Holonomic Systems by Lie Point Transformation

Jian-Le¹,

Feng-Xiang²

2012

J. mech.

View full text Add to dashboard Cite

In this paper, the conformal invariance and conserved quantities for higher-order holonomic systems are studied. Firstly, by establishing the differential equation of motion for the systems and introducing a one-parameter infinitesimal transformation group together with its infinitesimal generator vector, the determining equation of conformal invariance for the systems are provided, and the conformal factors expression are deduced. Secondly, the relation between conformal invariance and the Lie symmetry by the infinitesimal one-parameter point transformation group for the higher-order holonomic systems are deduced. Thirdly, the conserved quantities of the systems are derived using the structure equation satisfied by the gauge function. Lastly, an example of a higher-order holonomic mechanical system is discussed to illustrate these results.

show abstract

A conformal invariance for generalized Birkhoff equations

Cited by 26 publications

References 12 publications

Conformal invariance of Mei symmetry and conserved quantities of Lagrange equation of thin elastic rod

Conformal invariance of Mei symmetry and conserved quantities of Lagrange equation of thin elastic rod

Conformal Invariance and Conserved Quantities for Lagrange Equation of Thin Elastic Rod

Conformal Invariance and Conserved Quantity of the Higher-Order Holonomic Systems by Lie Point Transformation

Contact Info

Product

Resources

About