Conformal invariance and a kind of Hojman conserved quantity of the Nambu system

李燕,; 方建会,; 张克军,

doi:10.1088/1674-1056/20/3/030201

Cited by 8 publications

(4 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…4 of the symmetry algebra and subject it to various adjoint transformations to simplify it as much as possible. [29] The adjoint action is given by the Lie series (20) where…”

Section: Symmetry Reduction Methods and Optimal Systemmentioning

confidence: 99%

New exact solutions of the Einstein—Maxwell equations for magnetostatic fields

Goyal¹,

Gupta²

2012

Chinese Phys. B

View full text Add to dashboard Cite

The symmetry reduction method based on the Fréchet derivative of differential operators is applied to investigate symmetries of the Einstein-Maxwell field equations for magnetostatic fields, which is a coupled system of nonlinear partial differential equations of the second order. The technique yields invariant transformations that reduce the given system of partial differential equations to a system of nonlinear ordinary differential equations. Some of the reduced systems are further studied to obtain the exact solutions.

show abstract

“…4 of the symmetry algebra and subject it to various adjoint transformations to simplify it as much as possible. [29] The adjoint action is given by the Lie series (20) where…”

Section: Symmetry Reduction Methods and Optimal Systemmentioning

confidence: 99%

New exact solutions of the Einstein—Maxwell equations for magnetostatic fields

Goyal¹,

Gupta²

2012

Chinese Phys. B

View full text Add to dashboard Cite

show abstract

“…[50]. When α → 1, using conditions (33), the fractional Nambu equations (29) can be reduced to integer-order generalized Hamiltonian equations:…”

Section: The Relation Between a Fractional Nambu System And A Fractiomentioning

confidence: 99%

“…Ditto et al [21,22] presented the quantization problem of Nambu mechanics and indicated the validity of the fundamental identity of Nambu mechanics also at the quantum level. With the further developments in of science and technology, the Nambu dynamical system has played an important role not only in modern mechanics, but also in physics, engineering science, nonlinear science, celestial mechanics and so on [23][24][25][26][27][28][29][30][31][32][33]. However, no work had so far been published on the dynamics of Nambu systems with fractional derivative.…”

Section: Introductionmentioning

confidence: 99%

Fractional Nambu dynamics

Shao-Kai

2015

Acta Mech

View full text Add to dashboard Cite

In this paper, we present a new fractional dynamical theory, i.e., the dynamics of a Nambu system with fractional derivatives (the fractional Nambu dynamics), and study its applications to mechanical systems. By using the definition of combined fractional derivative, we construct unified fractional Nambu equations and, respectively, give four new kinds of fractional Nambu equations based on the different definitions of fractional derivative. Further, we study the relations between the fractional Nambu system, the fractional generalized Hamiltonian system, the fractional Birkhoffian system, the fractional Hamiltonian system, the fractional Lagrangian system and a series of integer-order dynamical systems and present the transformation conditions. And furthermore, as applications of the fractional Nambu method, we construct two kinds of fractional dynamical models, which include the fractional Euler-Poinsot model of rigid body which rotates with respect to a fixed point and the fractional Yamaleev oscillator model. This work provides a general method for studying a fractional dynamical problem which is related to science and engineering.

show abstract

“…The key question to the conformal invariance of dynamics is to find out the conformal factor. Considerable progress has been made over past years in the application of conformal invariance to mechanical systems [20][21][22][23][24][25]45]. However, the application of conformal invariance to thin elastic rod has never been investigated.…”

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

Conformal invariance and a kind of Hojman conserved quantity of the Nambu system

Cited by 8 publications

References 18 publications

New exact solutions of the Einstein—Maxwell equations for magnetostatic fields

New exact solutions of the Einstein—Maxwell equations for magnetostatic fields

Fractional Nambu dynamics

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

Contact Info

Product

Resources

About