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1.
MA Shan-Jun YANG Xue-Hui YANG Rong 《理论物理通讯》2006,46(2):309-312
Based on the three-order Lagrangian equation, pseudo-Hamilton actoon I^* is defined and the three-order Hamilton's principle and the conditions are obtained in the paper. Then, the Noether symmetry about three-order Lagrangian equations is deduced. Finally, an example is given to illustrate the application of the result. 相似文献
2.
In this paper, the general expressions of three-order Lagrangian equations in a motional coordinate system are obtained. In coordinate systems with some specific forms of motion, the expressions corresponding to these equations are also presented. 相似文献
3.
Variational principle and dynamical equations of discrete nonconservative holonomic systems
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By analogue with the methods and processes in continuous mechanics, a Lagrangian formulation and a Hamiltonian formulation of discrete mechanics are obtained. The dynamical equations
including Euler--Lagrange equations and Hamilton's canonical equations of the discrete nonconservative holonomic systems are derived on a discrete variational principle. Some illustrative
examples are also given. 相似文献
4.
Based on the infinitesimal and one parameter transformation,
the problem of Lie symmetry of three-order Lagrangian equations has
been studied. Under Lie transformation, the sufficient and necessary
condition which keeps three-order Lagrangian equations to be unchanged
and the invariant are obtained in this paper. 相似文献
5.
The Lagrangian function, the Hamiltonian function and the Rayleigh's dissipation function for the electrodynamic model of the rail plasma accelerator and for the phenomenon of polarization of plasma clusters have been found. The generalized momenta and energy, the Hamilton's canonical equations and the equation of energy balance have been derived in both cases. 相似文献
6.
ZHAO Hong-Xia MA Shan-Jun SHI Yong 《理论物理通讯》2008,49(2):479-481
In this paper, if the condition of variation δt=0 is satisfied, the higher-order Lagrangian equations and higher-order Hamilton's
equations, which show the consistency with the results of traditional analytical mechanics, are obtained from the higher-order Lagrangian equations and higher-order Hamilton's equations.
The results can enrich the theory of analytical mechanics. 相似文献
7.
研究了加速度线性相关的Lagrange函数,在加速度项系数对称的条件下,Lagrange方程保持为二阶微分方程;给出了从运动方程构造加速度相关的Lagrange函数的方法;研究同一系统的加速度相关和加速度无关的Lagrange函数之间的关系.举例说明结果的应用.
关键词:
Lagrange方程
加速度相关的Lagrange函数
广义力学
Lagrange函数的规范变换 相似文献
8.
The Helmholtz solution of the inverse problem for the variational calculus is used to study the analytic or Lagrangian structure of a number of nonlinear evolution equations. The quasilinear equations in the KdV hierarchy constitute a Lagrangian system. On the other hand, evolution equations with nonlinear dispersive terms (FNE) are non-Lagrangian. However, the method of Helmholtz can be judiciously exploited to construct Lagrangian system of such equations. In all cases the derived Lagrangians are gauge equivalent to those obtained earlier by the use of Hamilton’s variational principle supplemented by the methodology of integer-programming problem. The free Hamiltonian densities associated with the so-called gauge equivalent Lagrangians yield the equation of motion via a new canonical equation similar to that of Zakharov, Faddeev and Gardner. It is demonstrated that the Lagrangian system of FNE equations supports compacton solutions.PACS: 47.20.Ky; 42.81.Dp 相似文献
9.
论述用L定义光学的哈密顿H,并给出哈密顿公式的基本方程式,利用哈密顿方程式,在旋转对称的光学系统里追迹光线,并利用哈密顿公式得到折射面和透镜的简单结果。最后通过举例说明这个方法是可行的。 相似文献
10.
In this paper, we present the fractional Hamilton's canonical equations and the fractional non-Noether symmetry of Hamilton systems by the conformable fractional derivative. Firstly, the exchanging relationship between isochronous variation and fractional derivatives, and the fractional Hamilton principle of the system under this fractional derivative are proposed. Secondly, the fractional Hamilton's canonical equations of Hamilton systems based on the Hamilton principle are established. Thirdly, the fractional non-Noether symmetries, non-Noether theorem and non-Noether conserved quantities for the Hamilton systems with the conformable fractional derivatives are obtained. Finally, an example is given to illustrate the results. 相似文献
11.
Yong-Long Wang Chuan-Cong Wang Xue-Feng Ning Shu-Tao Ai Hong-Zhe Pan Tong-Song Jiang 《International Journal of Theoretical Physics》2008,47(9):2319-2325
For constrained Hamiltonian systems, the motion equations are deduced from total Hamiltonian and extended Hamiltonian with
Lagrangian multipliers depending on time t and canonical variables q
i
and p
i
. When the multipliers reduced to only depend on time t, the motion equations exactly agree with the old results. Under the same conditions (Lagrangian multipliers depend on time
t and canonical variables q
i
and p
i
), the relation equations of coefficients in the generator of gauge transformation are deduced, but the equations have an
additive term besides the well-known results. This additive term is from Lagrangian multipliers depending on canonical variables,
and it might perform the gauge symmetries that needs to be discussed further.
This project is supported by the fund of National Natural Science (10671086) and by National Laboratory for Superlattices
and Microstructures (CHJG200605). 相似文献
12.
Integrating factors and conservation theorems for Hamilton‘s canonical equations of motion of variable mass nonholonmic nonconservative dynamical systems 总被引:2,自引:0,他引:2
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We present a general approach to the construction of conservation laws for variable mass noholonmic nonconservative systems.First,we give the definition of integrating factors,and we study in detail the necessary conditions for the existence of the conserved quantities,Then,we establish the conservatioin theorem and its inverse theorem for Hamilton‘s canonical equations of motion of variable mass nonholonomic nonocnservative dynamical systems.Finally,we give an example to illustrate the application of the results. 相似文献
13.
We provide a model for an open invariant neighborhood of any orbit in a symplectic manifold endowed with a canonical proper symmetry. Our results generalize the constructions of Marle and Guillemin and Sternberg for canonical symmetries that have an associated momentum map. In these papers the momentum map played a crucial role in the construction of the tubular model. The present work shows that in the construction of the tubular model, the so-called Chu map, can be used instead, which exists for any canonical action, unlike the momentum map. Hamilton's equations for any invariant Hamiltonian function take on a particularly simple form in these tubular variables. As an application we will find situations, that we will call tubewise Hamiltonian, in which the existence of a standard momentum map in invariant neighborhoods is guaranteed. 相似文献
14.
Canonical formalism for SO(2) is developed. This group can be seen as a toy model of the Hamilton-Dirac mechanics with constraints.
The Lagrangian and Hamiltonian are explicitly constructed and their physical interpretations are given. The Euler-Lagrange
and Hamiltonian canonical equations coincide with the Lie equations. It is shown that the constraints satisfy CCR. Consistency
of the constraints is checked.
Presented at the International Colloquium “Integrable Systems and Quantum Symmetries”, Prague, 16–18 June 2005. 相似文献
15.
Several interacting models of chiral bosons and gauge fields are investigated on the noncommutative extended Minkowski spacetime which was recently proposed from a new point of view of disposing noncommutativity. The models include the bosonized chiral Schwinger model, the generalized chiral Schwinger model (GCSM) and its gauge invariant formulation. We establish the Lagrangian theories of the models, and then derive the Hamilton's equations in accordance with the Dirac's method and solve the equations of motion, and further analyze the self-duality of the Lagrangian theories in terms of the parent action approach. 相似文献
16.
基于热质理论,类比经典力学,给出了热质运动遵循的Hamilton原理以及相应的导热Lagrange方程.由于考虑了热质动能,热质运动的Hamilton原理有望应用于非Fourier效应的讨论,在忽略热质动能时,回归到Fourier热学.应用Lagrange方程对含内热源一维瞬态导热问题进行了近似求解,计算结果与解析解符合较好.从分析力学的角度对传热理论以及热学与力学的统一做了新的阐释,指出了现有文献中采用分析力学方法讨论导热问题时存在的某些不足,为导热问题的近似求解提供了新的思路,同时也说明了热质和热质能 相似文献
17.
Canonical symmetry properties of the constrained singular generalized mechanical system 总被引:1,自引:0,他引:1
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Based on generalized Apell-Chetaev constraint conditions and to take the inherent constrains for singular Lagrangian into account, the generalized canonical equations for a general mechanical system with a singular higher-order Lagrangian and subsidiary constrains are formulated. The canonical symmetries in phase space for such a system are studied and Noether theorem and its inversion theorem in the generalized canonical formalism have been established. 相似文献
18.
B. Talukdar S. Ghosh J. Shamanna P. Sarkar 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2002,21(1):105-108
It is shown that the usual Hamilton's variational principle supplemented by the methodology of the integer-programming problem
can be used to construct expressions for the Lagrangian densities of higher KdV fields. This is demonstrated with special
emphasis on the second and third members of the hierarchy. However, the method is general enough for applications to equations
of any order. The expressions for Lagrangian densities are used to calculate results for Hamiltonian densities that characterize
Zakharov-Faddeev-Gardner equation.
Received 27 January 2002 / Received in final form 6 May 2002 Published online 24 September 2002 相似文献
19.
T. Kawai 《Foundations of Physics》1975,5(1):143-158
Schwinger's action principle is formulated for the quantum system which corresponds to the classical system described by the LagrangianL
c(
, x)=(M/2)gij(x)
i
j–v(x). It is sufficient for the purpose of deriving the laws of quantum mechanics to consider onlyc-number variations of coordinates and time. The Euler-Lagrange equation, the canonical commutation relations, and the canonical equations of motion are derived from this principle in a consistent manner. Further, it is shown that an arbitrary point transformation leaves the forms of the fundamental equations invariant. The judicious choice of the quantal Lagrangian is essential in our formulation. A quantum mechanical analog of Noether's theorem, which relates the invariance of the quantal action with a conservation law, is established. The ambiguities in the quantal Lagrangian are also discussed and it is pointed out that the requirement of invariance is not sufficient to determine uniquely the quantal Lagrangian and the Hamiltonian. 相似文献
20.
CHEN Hang-Hui ZHENG Han-Qing 《理论物理通讯》2004,42(11)
A canonical formalism for Lagrangians of maximal nonlocality is established. The method is based on the familiar Legendre transformation to a new function, which can be derived from the maximally nonlocal Lagrangian.The corresponding canonical equations are derived through the standard procedure in local theory and appear much like those local ones, though the implication of the equations is largely expanded. 相似文献