Lie symmetry and Hojman conserved quantity of Nambu system

Peng, Lin; Fang, Jianhui; Ting, Pang

doi:10.1088/1674-1056/17/12/004

Chinese Phys. B

2008

DOI: 10.1088/1674-1056/17/12/004

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Lie symmetry and Hojman conserved quantity of Nambu system

Lin Peng

Jianhui Fang

Pang Ting

Abstract: This paper studies the Lie symmetry and Hojman conserved quantity of the Nambu system. The determining equations of Lie symmetry for the system are given. The conditions for existence and the form of the Hojman conserved quantity led by the Lie symmetry for the system are obtained. Finally, an example is given to illustrate the application of the results.

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Cited by 7 publications

References 16 publications

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Fractional Nambu dynamics

Shao-Kai

2015

Acta Mech

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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.

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Fractional Nambu dynamics

Shao-Kai

2015

Acta Mech

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

李燕¹,

方建会²,

张克军³

2011

Chinese Phys. B

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Conformal invariance and a kind of Hojman conserved quantity of the Nambu system under infinitesimal transformations are studied. The definition and the determining equation of conformal invariance of the system are presented. The necessary and sufficient condition under which the conformal invariance of the system would have Lie symmetry under infinitesimal transformations is derived. Then, the condition of existence and a kind of Hojman conserved quantity are obtained. Finally, an example is given to illustrate the application of the results.

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A new type of conserved quantity of Mei symmetry for the motion of mechanico—electrical coupling dynamical systems

Zhao¹,

Fu²,

Chen³

2011

Chinese Phys. B

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We obtain a new type of conserved quantity of Mei symmetry for the motion of mechanico-electrical coupling dynamical systems under the infinitesimal transformations. A criterion of Mei symmetry for the mechanico-electrical coupling dynamical systems is given. Simultaneously, the condition of existence of the new conserved quantity of Mei symmetry for mechanico-electrical coupling dynamical systems is obtained. Finally, an example is given to illustrate the application of the results.

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Lie symmetry and Hojman conserved quantity of Nambu system

Cited by 7 publications

References 16 publications

Fractional Nambu dynamics

Fractional Nambu dynamics

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

A new type of conserved quantity of Mei symmetry for the motion of mechanico—electrical coupling dynamical systems

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