广义Birkhoff系统的一类积分

将Birkhoff方程添加一附加项成为广义Birkhoff方程.将Birkhoff方程的一类积分推广并应用于广义Birkhoff方程.举例说明结果的应用. 关键词： Birkhoff方程 广义Birkhoff方程 积分     

广义Birkhoff方程的积分方法

场方法和最终乘子法是求解运动微分方程的基本方法.本文将这两种方法应用于广义Birkhoff系统,求出了场方法的基本偏微分方程和该方程的完全积分;根据Jacobi最终乘子定理求出了广义Birkhoff方程的解.并举例说明结果的应用.     

广义Birkhoff系统的两类广义梯度表示

提出了两类广义梯度系统, 即广义斜梯度系统以及具有对称负定矩阵的广义梯度系统. 分别讨论了这两类梯度系统与动力学系统稳定性的关系. 研究了广义Brikhoff系统的两类广义梯度表示, 分别给出条件和表达式. 给出了广义Brikhoff系统稳定性的梯度判别法, 利用广义梯度系统的性质来研究广义Birkhoff系统的稳定性. 并举例说明了方法的应用.     

一类广义Birkhoff系统的广义正则变换

研究一类广义Birkhoff系统的广义正则变换.建立这类广义Birkhoff系统的运动微分方程,得到了该系统的广义正则变换以及保持广义正则变换的条件.最后,举例说明结果的应用.     

Algebraic structure and Poisson integrals of a rotational relativistic Birkhoff system

We have studied the algebraic structure of the dynamical equations of a rotational relativistic Birkhoff system. It is proven that autonomous and semi-autonomous rotational relativistic Birkhoff equations possess consistent algebraic structure and Lie algebraic structure. In general, non-autonomous rotational relativistic Birkhoff equations possess no algebraic structure, but a type of special non-autonomous rotational relativistic Birkhoff equation possesses consistent algebraic structure and consistent Lie algebraic structure. Then, we obtain the Poisson integrals of the dynamical equations of the rotational relativistic Birkhoff system. Finally, we give an example to illustrate the application of the results.     

一类广义Birkhoff系统的无限小正则变换与积分

研究一类广义Birkhoff系统的无限小正则变换与积分, 建立这类广义Birkhoff系统的方程,将Birkhoff系统的无限小正则变换与积分的有关结果推广到这类广义Birkhoff系统,举例说明结果的应用.     

广义Pfaff-Birkhoff-d'Alembert原理与广义Birkhoff系统的形式不变性

研究了广义Pfaff-Birkhoff-d'Alembert原理和广义Birkhoff系统在群的无限小变换下的形式不变性质.给出了形式不变性的判据,并由形式不变性导出Noether守恒量和新型守恒量.     

Stability for manifolds of equilibrium states of generalized Birkhoff system

<正>Stability for the manifolds of equilibrium states of a generalized Birkhoff system is studied.A theorem for the stability of the manifolds of equilibrium states of the general autonomous system is used to the generalized Birkhoffian system and two propositions on the stability of the manifolds of equilibrium states of the system are obtained.An example is given to illustrate the application of the results.     

A finite difference beam propagation algorithm based on generalized transmission line equations

A wide angle beam propagation algorithm is presented, which is based on generalized transmission line (GTL) equations. Besides the discretization, no further approximation is introduced. In principle, a full vectorial analysis is possible, and anisotropic material can be taken into account. The algorithm has been verified for planar 2D-waveguide devices. The wide angle characteristic has been examined by determining the propagation of tilted Gaussian beams in homogeneous media. Further studies were performed for tilted waveguides and for taper structures. Results for the latter devices were compared with other methods showing a very good agreement.     

广义经典力学中Hamilton-Tabarrok-Leech正则方程的对称性理论

提出广义Hamilton-Tabarrok-Leech正则方程的对称性理论.列写系统的运动方程.研究系统的Noether对称性、形式不变性和Lie对称性，并求出相应的守恒量.举例说明结果的应用. 关键词： 广义经典力学 H-T-L 正则方程 对称性 守恒量     

广义Birkhoff系统动力学的一类逆问题

针对广义Birkhoff系统动力学,提出广义Birkhoff系统动力学的一类逆问题,研究由已知积分流形来建立广义Birkhoff方程. 这类逆问题的解通常不是唯一的,需给出必要的补充要求. 最后举例说明结果的应用. 关键词： 广义Birkhoff系统 动力学逆问题 积分流形     

广义Birkhoff系统的时间积分定理

研究了广义Birkhoff系统的时间积分定理.给出系统的时间积分等式,并由此等式导出类能量方程、类维里定理、一个积分变分原理和一个微分变分原理. 关键词： 广义Birkhoff系统 时间积分定理 类能量方程 变分原理     

Determination of the Electromagnetic Lagrangian from a System of Poisson Brackets

The Lagrangian and Hamiltonian formulations of electromagnetism are reviewed and the Maxwell equations are obtained from the Hamiltonian for a system of many electric charges. It is shown that three of the equations which were obtained from the Hamiltonian, namely the Lorentz force law and two Maxwell equations, can be obtained as well from a set of postulated Poisson brackets. It is shown how the results derived from these brackets can be used to reconstruct the original Lagrangian for the theory aided by some reasoning based on physical concepts.     

Noether's theory of generalized linear nonholonomic mechanical systems

By introducing the quasi-symmetry of the infinitesimal transformation of the transformation group G_r, the Noether's theorem and the Noether's inverse theorem for generalized linear nonholonomic mechanical systems are obtained in a generalized compound derivative space. An example is given to illustrate the application of the result.     

Poisson theory and integration method for a dynamical system of relative motion

This paper focuses on studying the Poisson theory and the integration method of dynamics of relative motion.Equations of a dynamical system of relative motion in phase space are given.Poisson theory of the system is established.The Jacobi last multiplier of the system is defined,and the relation between the Jacobi last multiplier and the first integrals of the system is studied.Our research shows that for a dynamical system of relative motion,whose configuration is determined by n generalized coordinates,the solution of the system can be found by using the Jacobi last multiplier if (2n 1) first integrals of the system are known.At the end of the paper,an example is given to illustrate the application of the results.     

Formal Poisson Cohomology of Quadratic Poisson Structures

We compute the formal Poisson cohomology of quadratic Poisson structures. We first recall that, generically, quadratic Poisson structures are diagonalizable. Then we compute the formal cohomology of diagonal Poisson structures.     

New approach for analysing master equations of generalized phase diffusion models in the entangled state representation

By virtue of the well-behaved properties of the bipartite entangled states representation, this paper analyse and solves some master equations for generalized phase diffusion models, which seems concise and effective. This method can also be applied to solve other master equations.     

广义Birkhoff自治系统平衡状态的流形稳定性

研究广义Birkhoff自治系统平衡状态流形稳定性.建立广义Birkhoff自治系统的受绕运动方程和平衡方程.由Liapunov稳定性理论给出广义Birkhoff自治系统的平衡状态流形稳定性的有关判据.举例说明结果的应用.     

Existence theory of the linear equations appearing in the Chapman-Enskog solutions to two kinetic equations for liquids

The linear operators appearing in the Chapman-Enskog solutions to Kirkwood's Fokker-Planck kinetic equation and to Rice and Allnatt's kinetic equation are studied in this article. Existence proofs are given for the linearized Chapman-Enskog equations involving either the Fokker-Planck or the Rice-Allnatt operators. It is shown that the Fokker-Planck and Rice-Allnatt operators, defined in the domain appropriate to kinetic theory, are essentially self-adjoint. It is also shown that the spectrum of either of these operators coincides with the spectrum of the self-adjoint extension of the corresponding operator.Sloan Foundation Fellow 1968–70. Guggenheim Fellow 1969–70.     

New exact travelling wave solutions of the generalized zakharov equations

A direct algebraic method is introduced for constructing exact travelling wave solutions of nonlinear partial differential equations with complex phases. The scheme is implemented for obtaining multiple soliton solutions of the generalized Zakharov equations, and then new exact travelling wave solutions with complex phases are obtained. In addition, by using new exact solutions of an auxiliary ordinary differential equation, new exact travelling wave solutions for the generalized Zakharov equations are obtained.