scholarly journals On Mei symmetry of Lagrangian system and Hamiltonian system

2005 ◽  
Vol 54 (2) ◽  
pp. 496
Author(s):  
Fang Jian-Hui ◽  
Peng Yong ◽  
Liao Yong-Pan
Keyword(s):  
Hamiltonian System ◽  
Lagrangian System ◽  
Mei Symmetry

Mei Symmetry and Lie Symmetry of Relativistic Hamiltonian System

2004 ◽  
Vol 42 (1) ◽  
pp. 19-22 ◽  
Author(s):  
Fang Jian-Hui ◽  
Yan Xiang-Hong ◽  
Li Hong ◽  
Chen Pei-Sheng
Keyword(s):  
Hamiltonian System ◽  
Lie Symmetry ◽  
Mei Symmetry

scholarly journals Mei Symmetry and New Conserved Quantities of Time-Scale Birkhoff’s Equations

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Xiang-Hua Zhai ◽  
Yi Zhang
Keyword(s):  
Hamiltonian System ◽  
Time Scales ◽  
Time Scale ◽  
Dynamic Equations ◽  
Conserved Quantities ◽  
Dynamical Processes ◽  
Birkhoffian System ◽  
Special Case ◽  
Mei Symmetry

The time-scale dynamic equations play an important role in modeling complex dynamical processes. In this paper, the Mei symmetry and new conserved quantities of time-scale Birkhoff’s equations are studied. The definition and criterion of the Mei symmetry of the Birkhoffian system on time scales are given. The conditions and forms of new conserved quantities which are found from the Mei symmetry of the system are derived. As a special case, the Mei symmetry of time-scale Hamilton canonical equations is discussed and new conserved quantities for the Hamiltonian system on time scales are derived. Two examples are given to illustrate the application of results.

scholarly journals Type Ⅲ structural equation and Mei conserved quantity of Mei symmetry for a Lagrangian system

2010 ◽  
Vol 59 (5) ◽  
pp. 2939
Author(s):  
Jia Li-Qun ◽  
Zhang Yao-Yu ◽  
Yang Xin-Fang ◽  
Cui Jin-Chao ◽  
Xie Yin-Li
Keyword(s):  
Structural Equation ◽  
Conserved Quantity ◽  
Lagrangian System ◽  
Mei Symmetry

On New Analytic Free Vibration Solutions of Doubly Curved Shallow Shells by the Symplectic Superposition Method Within the Hamiltonian-System Framework

2020 ◽  
Vol 143 (1) ◽  
Author(s):  
Rui Li ◽  
Chao Zhou ◽  
Xinran Zheng
Keyword(s):  
Hamiltonian System ◽  
Free Vibration ◽  
Original Problem ◽  
Analytic Solutions ◽  
Solution Procedure ◽  
Symplectic Space ◽  
Lagrangian System ◽  
Superposition Method ◽  
Shallow Shells ◽  
Doubly Curved

Abstract This study presents a first attempt to explore new analytic free vibration solutions of doubly curved shallow shells by the symplectic superposition method, with focus on non-Lévy-type shells that are hard to tackle by classical analytic methods due to the intractable boundary-value problems of high-order partial differential equations. Compared with the conventional Lagrangian-system-based expression to be solved in the Euclidean space, the present description of the problems is within the Hamiltonian system, with the solution procedure implemented in the symplectic space, incorporating formulation of a symplectic eigenvalue problem and symplectic eigen expansion. Specifically, an original problem is first converted into two subproblems, which are solved by the above strategy to yield the symplectic solutions. The analytic frequency and mode shape solutions are then obtained by the requirement of the equivalence between the original problem and the superposition of subproblems. Comprehensive results for representative non-Lévy-type shells are tabulated or plotted, all of which are well validated by satisfactory agreement with the numerical finite element method. Due to the strictness of mathematical derivation and accuracy of solution, the developed method provides a solid approach for seeking more analytic solutions.

scholarly journals Hamiltonian Approach to Magnetic Fields with Toroidal Surfaces

1985 ◽  
Vol 40 (10) ◽  
pp. 959-967
Author(s):  
A. Salat
Keyword(s):  
Magnetic Field ◽  
Hamiltonian System ◽  
Magnetic Fields ◽  
Constant Pressure ◽  
Time Dependent ◽  
Hamiltonian Approach ◽  
One Dimensional ◽  
Mhd Equilibrium ◽  
Magnetic Surfaces ◽  
Rotational Transform

The equivalence of magnetic field line equations to a one-dimensional time-dependent Hamiltonian system is used to construct magnetic fields with arbitrary toroidal magnetic surfaces I = const. For this purpose Hamiltonians H which together with their invariants satisfy periodicity constraints have to be known. The choice of H fixes the rotational transform η(I). Arbitrary axisymmetric fields, and nonaxisymmetric fields with constant η(I) are considered in detail.Configurations with coinciding magnetic and current density surfaces are obtained. The approach used is not well suited, however, to satisfying the additional MHD equilibrium condition of constant pressure on magnetic surfaces.

Dynamic Buckling of Cylindrical Shells under Axial Impact in Hamiltonian System

2012 ◽  
Vol 13 (1) ◽  
Author(s):  
Jia-Bin Sun ◽  
Xin-Sheng Xu ◽  
Chee-Wah Lim
Keyword(s):  
Hamiltonian System ◽  
Critical Load ◽  
Impact Load ◽  
Dynamic Buckling ◽  
Inertia Force ◽  
Elastic Cylindrical Shell ◽  
Symplectic Method ◽  
Buckling Mode ◽  
Axial Impact ◽  
Dual Variables

AbstractIn this paper, the dynamic buckling of an elastic cylindrical shell subjected to an axial impact load is analyzed in Hamiltonian system. By employing a symplectic method, the traditional governing equations are transformed into Hamiltonian canonical equations in dual variables. In this system, the critical load and buckling mode are reduced to solving symplectic eigenvalues and eigensolutions respectively. The result shows that the critical load relates with boundary conditions, thickness of the shell and radial inertia force. And the corresponding buckling modes present some local shapes. Besides, the process of dynamic buckling is related to the stress wave, the critical load and buckling mode depend upon the impacted time. This paper gives analytically and numerically some new rules of the buckling problem, which is useful for designing shell structures.

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