The Experts below are selected from a list of 177 Experts worldwide ranked by ideXlab platform

Shao-kai Luo - One of the best experts on this subject based on the ideXlab platform.

  • A new Lie symmetrical method of finding conserved quantity for Birkhoffian systems
    Nonlinear Dynamics, 2012
    Co-Authors: Shao-kai Luo
    Abstract:

    For a Birkhoffian system, a new Lie symmetrical method to find a conserved quantity is given. Based on the invariance of the equations of motion for the system under a general Infinitesimal Transformation of Lie groups, the Lie symmetrical determining equations are obtained. Then, several important relationships which reveal the interior properties of the Birkhoffian system are given. By using these relationships, a new Lie symmetrical conservation law for the Birkhoffian system is presented. The new conserved quantity is constructed in terms of Infinitesimal generators of the Lie symmetry and the system itself without solving the structural equation which may be very difficult to solve. Furthermore, several deductions are given in the special Infinitesimal Transformations and the results are reduced to a Hamiltonian system. Finally, one example is given to illustrate the method and results of the application.

  • Lie symmetrical perturbation and a new type of non-Noether adiabatic invariants for disturbed generalized Birkhoffian systems
    Nonlinear Dynamics, 2011
    Co-Authors: Wenan Jiang, Shao-kai Luo
    Abstract:

    For a generalized Birkhoffian system with the action of small disturbance, the Lie symmetrical perturbation and a new type of non-Noether adiabatic invariants are presented. On the basis of the invariance of disturbed generalized Birkhoffian system under general Infinitesimal Transformation of group, the determining equation of Lie symmetrical perturbation of the system is constructed. Based on the definition of higher-order adiabatic invariants of a mechanical system, a new type of non-Noether adiabatic invariants of a disturbed generalized Birkhoffian system is obtained by investigating the Lie symmetrical perturbation. Then, a new type of exact invariants of non-Noether type is given, furthermore adiabatic invariants and exact invariants of non-Noether type are obtained under the special Infinitesimal Transformation of group. Finally, an example is given to illustrate the application of the method and results.

  • A new type of non-Noether exact invariants and adiabatic invariants of generalized Hamiltonian systems
    Nonlinear Dynamics, 2011
    Co-Authors: Wenan Jiang, Shao-kai Luo
    Abstract:

    For a generalized Hamiltonian system with the action of small forces of perturbation, the Lie symmetries, symmetrical perturbation, and adiabatic invariants is presented. Based on the invariance of equations of motion for the system under general Infinitesimal Transformation of Lie groups, the Lie symmetrical determining equations, and exact invariants of the system are given. Then the determining equations of Lie symmetrical perturbation and adiabatic invariants of the disturbed systems are obtained. Furthermore, in the special Infinitesimal Transformations, two deductions are given. At the end of the paper, one example is given to illustrate the application of the method and result.

Wenan Jiang - One of the best experts on this subject based on the ideXlab platform.

  • Conformal Invariance and Conserved Quantities of Nonmaterial Volumes
    Reports on Mathematical Physics, 2019
    Co-Authors: Kun Liu, Wenan Jiang, Yu Gao, Zhao-wang Xia
    Abstract:

    This paper investigates conformal invariance and conserved quantities of nonmaterial volumes. An Infinitesimal Transformation group and Infinitesimal Transformations vectors of generators are proposed. The definition of conformal invariance and the determining equation for the systems are presented. The necessary and sufficient conditions of conformal invariance being Noether symmetrical simultaneously by the action of Infinitesimal Transformations are given. The conformal factor is deduced from the conformal invariance and Noether symmetry. The corresponding Noether conserved quantities are derived with the aid of a structure equation. Three examples are given to illustrate application of the method, the corresponding conserved quantities are obtained under the conformal invariance and Noether symmetry.

  • Symmetry and conserved quantities for non-material volumes
    Acta Mechanica, 2017
    Co-Authors: Wenan Jiang, Li-li Xia
    Abstract:

    This paper investigates the Lie symmetry and conserved quantities of non-material volumes. The Lie symmetrical determining equations of the system are presented by introducing the invariance of equations of motion for the system under general Infinitesimal Transformation of Lie groups. The structure equations and the form of conserved quantities are calculated. And three kinds of conserved quantities, i.e., Noether, Lutzky and Mei conserved quantities of the systems, are derived. In addition, the Hojman conserved quantity of the systems is proposed under the special Infinitesimal Transformations. An example is given to illustrate the application of the method and result, and four kinds of conserved quantities are obtained under the Lie symmetrical Transformations.

  • lie symmetries symmetrical perturbation and a new adiabatic invariant for disturbed nonholonomic systems
    Nonlinear Dynamics, 2012
    Co-Authors: Zhuangjun Li, Wenan Jiang
    Abstract:

    For a nonlinear nonholonomic constrained mechanical system with the action of small forces of perturbation, Lie symmetries, symmetrical perturbation, and a new type of non-Noether adiabatic invariants are presented in general Infinitesimal Transformation of Lie groups. Based on the invariance of the equations of motion for the system under general Infinitesimal Transformation of Lie groups, the Lie symmetrical determining equations, constraints restriction equations, additional restriction equations, and exact invariants of the system are given. Then, under the action of small forces of perturbation, the determining equations, constraints restriction equations, and additional restriction equations of the Lie symmetrical perturbation are obtained, and adiabatic invariants of the Lie symmetrical perturbation, the weakly Lie symmetrical perturbation, and the strongly Lie symmetrical perturbation for the disturbed nonholonomic system are obtained, respectively. Furthermore, a set of non-Noether exact invariants and adiabatic invariants are given in the special Infinitesimal Transformations. Finally, one example is given to illustrate the application of the method and results.

  • Lie symmetrical perturbation and a new type of non-Noether adiabatic invariants for disturbed generalized Birkhoffian systems
    Nonlinear Dynamics, 2011
    Co-Authors: Wenan Jiang, Shao-kai Luo
    Abstract:

    For a generalized Birkhoffian system with the action of small disturbance, the Lie symmetrical perturbation and a new type of non-Noether adiabatic invariants are presented. On the basis of the invariance of disturbed generalized Birkhoffian system under general Infinitesimal Transformation of group, the determining equation of Lie symmetrical perturbation of the system is constructed. Based on the definition of higher-order adiabatic invariants of a mechanical system, a new type of non-Noether adiabatic invariants of a disturbed generalized Birkhoffian system is obtained by investigating the Lie symmetrical perturbation. Then, a new type of exact invariants of non-Noether type is given, furthermore adiabatic invariants and exact invariants of non-Noether type are obtained under the special Infinitesimal Transformation of group. Finally, an example is given to illustrate the application of the method and results.

  • A new type of non-Noether exact invariants and adiabatic invariants of generalized Hamiltonian systems
    Nonlinear Dynamics, 2011
    Co-Authors: Wenan Jiang, Shao-kai Luo
    Abstract:

    For a generalized Hamiltonian system with the action of small forces of perturbation, the Lie symmetries, symmetrical perturbation, and adiabatic invariants is presented. Based on the invariance of equations of motion for the system under general Infinitesimal Transformation of Lie groups, the Lie symmetrical determining equations, and exact invariants of the system are given. Then the determining equations of Lie symmetrical perturbation and adiabatic invariants of the disturbed systems are obtained. Furthermore, in the special Infinitesimal Transformations, two deductions are given. At the end of the paper, one example is given to illustrate the application of the method and result.

Fu Jing-li - One of the best experts on this subject based on the ideXlab platform.

  • Conformal invariance and Hojman conserved quantities for holonomic systems with quasi-coordinates
    Chinese Physics B, 2010
    Co-Authors: Luo Yi-ping, Fu Jing-li
    Abstract:

    We propose a new concept of the conformal invariance and the conserved quantities for holonomic systems with quasi-coordinates. A one-parameter Infinitesimal Transformation group and its Infinitesimal Transformation vector of generators for holonomic systems with quasi-coordinates are described in detail. The conformal factor in the determining equations of the Lie symmetry is found. The necessary and sufficient conditions of conformal invariance, which are simultaneously of Lie symmetry, are given. The conformal invariance may lead to corresponding Hojman conserved quantities when the conformal invariance satisfies some conditions. Finally, an illustration example is introduced to demonstrate the application of the result.

  • Structure properties and Noether symmetries for super-long elastic slender rod ⁄
    Chinese Physics B, 2008
    Co-Authors: Fu Jing-li, Zhao Wei-jia, Weng Yu-quan
    Abstract:

    DNA is a nucleic acid molecule with double-helical structures that are special symmetrical structures attracting great attention of numerous researchers. The super-long elastic slender rod, an important structural model of DNA and other long-train molecules, is a useful tool in analysing the symmetrical properties and the stabilities of DNA. This paper studies the structural properties of a super-long elastic slender rod as a structural model of DNA by using Kirchhoff's analogue technique and presents the Noether symmetries of the model by using the method of Infinitesimal Transformation. Based on Kirchhoff's analogue it analyses the generalized Hamilton canonical equations. The Infinitesimal Transformations with respect to the radial coordinate, the generalized coordinates, and the quasi-momenta of the model are introduced. The Noether symmetries and conserved quantities of the model are obtained.

  • Lie Symmetries and Conserved Quantities for Super-Long Elastic Slender Rod
    Chinese Physics Letters, 2007
    Co-Authors: Zhao Wei-jia, Weng Yu-quan, Fu Jing-li
    Abstract:

    DNA is a nucleic acid molecule with double-helical structures that are special symmetrical structures attracting great attention of numerous researchers. The super-long elastic slender rod, an important structural model of DNA and other long-train molecules, is a useful tool in analysing the symmetrical properties and the stabilities of DNA. We study the Lie symmetries of a super-long elastic slender rod by using the methods of Infinitesimal Transformation. Based on Kirchhoff's analogue, generalized Hamilton canonical equations are analysed. The Infinitesimal Transformations with respect to the radian coordinate, the generalized coordinate, and the quasi-momentum of the model are introduced. The Lie symmetries and conserved quantities of the model are presented.

  • Localized Lie symmetries and conserved quantities for the finite-degree-of-freedom systems
    Chinese Physics, 2004
    Co-Authors: Fu Jing-li, Chen Li-qun, Bai Jing-hua
    Abstract:

    This paper focuses on the study of localized Lie symmetries under the Infinitesimal Transformation of an infinite continuous group for the finite-degree-of-freedom systems. Based on an invariance of differential equation under an Infinitesimal Transformation, we present the localized Lie symmetries including direct and inverse problems for the finite degree-of-freedom mechanical systems. We also give the definitions, determining equations, structural equation and conserved laws of localized Lie symmetries and further, the Lie symmetries under the Infinitesimal Transformation of a finite continuous group derived from localized Lie symmetry. Finally, an example is discussed to illustrate these results.

Zhuangjun Li - One of the best experts on this subject based on the ideXlab platform.

  • a new lie symmetrical method of finding a conserved quantity for a dynamical system in phase space
    Acta Mechanica, 2012
    Co-Authors: Zhuangjun Li, Lin Li
    Abstract:

    For a dynamical system in phase space, a new Lie symmetrical method to find a conserved quantity is presented in a general Infinitesimal Transformation of Lie groups. Based on the invariance of the differential equations of motion for the system under a general Infinitesimal Transformation of Lie groups, the Lie symmetrical determining equations are obtained. Then, an important relationship that reveals the interior properties of a dynamical system in phase space is given. By using the relationship, a Lie symmetrical basic integral variable relation and a new Lie symmetrical conservation law for the dynamical system in phase space are given. The new conserved quantity is constructed in terms of the Infinitesimal generators of Lie symmetry and the system itself without solving the structural equation. Furthermore, the method is applied in the Hamiltonian system, the nonconservative Hamiltonian system and the nonholonomic Hamiltonian system. Finally, one example is given to illustrate the method and results of the application.

  • lie symmetries symmetrical perturbation and a new adiabatic invariant for disturbed nonholonomic systems
    Nonlinear Dynamics, 2012
    Co-Authors: Zhuangjun Li, Wenan Jiang
    Abstract:

    For a nonlinear nonholonomic constrained mechanical system with the action of small forces of perturbation, Lie symmetries, symmetrical perturbation, and a new type of non-Noether adiabatic invariants are presented in general Infinitesimal Transformation of Lie groups. Based on the invariance of the equations of motion for the system under general Infinitesimal Transformation of Lie groups, the Lie symmetrical determining equations, constraints restriction equations, additional restriction equations, and exact invariants of the system are given. Then, under the action of small forces of perturbation, the determining equations, constraints restriction equations, and additional restriction equations of the Lie symmetrical perturbation are obtained, and adiabatic invariants of the Lie symmetrical perturbation, the weakly Lie symmetrical perturbation, and the strongly Lie symmetrical perturbation for the disturbed nonholonomic system are obtained, respectively. Furthermore, a set of non-Noether exact invariants and adiabatic invariants are given in the special Infinitesimal Transformations. Finally, one example is given to illustrate the application of the method and results.

Weng Yu-quan - One of the best experts on this subject based on the ideXlab platform.

  • Structure properties and Noether symmetries for super-long elastic slender rod ⁄
    Chinese Physics B, 2008
    Co-Authors: Fu Jing-li, Zhao Wei-jia, Weng Yu-quan
    Abstract:

    DNA is a nucleic acid molecule with double-helical structures that are special symmetrical structures attracting great attention of numerous researchers. The super-long elastic slender rod, an important structural model of DNA and other long-train molecules, is a useful tool in analysing the symmetrical properties and the stabilities of DNA. This paper studies the structural properties of a super-long elastic slender rod as a structural model of DNA by using Kirchhoff's analogue technique and presents the Noether symmetries of the model by using the method of Infinitesimal Transformation. Based on Kirchhoff's analogue it analyses the generalized Hamilton canonical equations. The Infinitesimal Transformations with respect to the radial coordinate, the generalized coordinates, and the quasi-momenta of the model are introduced. The Noether symmetries and conserved quantities of the model are obtained.

  • Lie Symmetries and Conserved Quantities for Super-Long Elastic Slender Rod
    Chinese Physics Letters, 2007
    Co-Authors: Zhao Wei-jia, Weng Yu-quan, Fu Jing-li
    Abstract:

    DNA is a nucleic acid molecule with double-helical structures that are special symmetrical structures attracting great attention of numerous researchers. The super-long elastic slender rod, an important structural model of DNA and other long-train molecules, is a useful tool in analysing the symmetrical properties and the stabilities of DNA. We study the Lie symmetries of a super-long elastic slender rod by using the methods of Infinitesimal Transformation. Based on Kirchhoff's analogue, generalized Hamilton canonical equations are analysed. The Infinitesimal Transformations with respect to the radian coordinate, the generalized coordinate, and the quasi-momentum of the model are introduced. The Lie symmetries and conserved quantities of the model are presented.