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1.
The purpose of this paper is to provide a new method called the
Lagrange--Noether method for solving second-order differential
equations. The method is, firstly, to write the second-order
differential equations completely or partially in the form of
Lagrange equations, and secondly, to obtain the integrals of the
equations by using the Noether theory of the Lagrange system. An
example is given to illustrate the application of the result. 相似文献
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3.
Methods of analytical mechanics for solving differential equations of first order 总被引:5,自引:0,他引:5 下载免费PDF全文
A differential equation of first order can be expressed by the equation of motion of a mechanical system. In this paper, three methods of analytical mechanics, i.e. the Hamilton--Noether method, the
Lagrange--Noether method and the Poisson method, are given to solve a differential equation of first order, of which the way may be called the mechanical methodology in mathematics. 相似文献
4.
This paper studies a conformal invariance and an integration of first-order differential equations. It obtains the corresponding infinitesimal generators of conformal invariance by using the symmetry of the differential equations, and expresses the differential equations by the equations of a Birkhoff system or a generalized Birkhoff system. If the infinitesimal generators are those of a Noether symmetry, the conserved quantity can be obtained by using the Noether theory of the Birkhoff system or the generalized Birkhoff system. 相似文献
5.
用场方法来求解Whittaker方程.将一个场变量取作为其余场变量和时间的函数并对这个函数建立基本偏微方程.如能求得它的完全积分,那么Whittaker方程的解可由解代数方程来得到.
关键词:
场变量
基本偏微分方程
场方法
积分 相似文献
6.
The Hamilton--Jacobi method for solving ordinary differential equations is presented
in this paper. A system of ordinary differential equations of first order or second
order can be expressed as a Hamilton system under certain conditions. Then the
Hamilton--Jacobi method is used in the integration of the Hamilton system and the
solution of the original ordinary differential equations can be found. Finally, an
example is given to illustrate the application of the result. 相似文献
7.
研究事件空间中Birkhoff系统动力学.在(2n+1)维事件空间中,建立了Birkhoff系统的Pfaff-Birkhoff-d'Alembert原理和Birkhoff参数方程,研究了方程的第一积分,给出了第一积分及其存在条件.
关键词:
Birkhoff系统
事件空间
参数方程
第一积分 相似文献
8.
Construction of the solution of variational equations for constrained Birkhoffian systems 总被引:3,自引:0,他引:3 下载免费PDF全文
In this paper we present the variational equations of constrained Birkhoffian systems and study their solution.It is proven that,under some conditions,a particular solution of variational equations can be obtained by using a first integral.At the end of the paper,an example is given to illustrate the application of the results. 相似文献
9.
The stability of second-order differential equations is studied by using
their integrals. A system of second-order differential equations can be
considered as a mechanical system with holonomic constraints. A conserved
quantity of the mechanical system or a part of the system is obtained by
using the Noether theory. It is possible that the conserved quantity becomes
a Liapunov function and the stability of the system is proved by the
Liapunov theorem. 相似文献
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11.
This paper is intended to apply the potential integration method to the differential equations of the Birkhoffian system. The method is that, for a given Birkhoffian system, its differential equations are first rewritten as 2n first-order differential equations. Secondly, the corresponding partial differential equations are obtained by potential integration method and the solution is expressed as a complete integral. Finally, the integral of the system is obtained. 相似文献
12.
We study the existence of local analytic first integrals of a class of analytic differential systems in the plane, obtained from the Chua?s system studied in L.O. Chua (1992, 1995), N.V. Kuznetsov et al. (2011), G.A. Leonov et al. (2012) , , and . The method used can be applied to other analytic differential systems. 相似文献
13.
介绍了蒙特卡罗方法的基本原理以及随机数的产生方法。基于蒙特卡罗方法的思想,结合有限差分方法,建立了求解微分方程边值问题的随机概率模型,并以第一类边界条件的拉普拉斯方程和一个给定初值及边界条件的非稳态热传导方程为数值算例,研究了蒙特卡罗方法在求解微分方程边值问题中的应用。结果表明:利用蒙特卡罗方法,不仅可以有效解决给定边界条件的微分方程,对于给定初值条件的微分方程,也可以从时域有限差分方程出发,采用蒙特卡罗方法进行求解。数值模拟和对误差的理论分析均表明,增加蒙特卡罗试验中的模拟粒子点数,可以提高计算结果的精度。 相似文献
14.
We extend techniques developed for the study of turbulent fluid flows to the statistical study of the dynamics of differential delay equations. Because the phase spaces of differential delay equations are infinite dimensional, phase-space densities for these systems are functionals. We derive a Hopf-like functional differential equation governing the evolution of these densities. The functional differential equation is reduced to an infinite chain of linear partial differential equations using perturbation theory. A necessary condition for a measure to be invariant under the action of a nonlinear differential delay equation is given. Finally, we show that the evolution equation for the density functional is the Fourier transform of the infinite-dimensional version of the Kramers-Moyal expansion. 相似文献
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16.
LUO Shao-Kai 《理论物理通讯》2003,40(8)
For a relativistic Birkhoffian system, the first integrals and the construction of integral invariants arestudied. Firstly, the cyclic integrals and the generalized energy integral of the system are found by using the perfectdifferential method. Secondly, the equations of nonsimultaneous variation of the system are established by using therelation between the simultaneous variation and the nonsimultaneous variation. Thirdly, the relation between the firstintegral and the integral invariant of the system is studied, and it is proved that, using a first integral, we can construct anintegral invariant of the system. Finally, the relation between the relativistic Birkhoffian dynamics and the relativisticHamiltonian dynamics is discussed, and the first integrals and the integral invariants of the relativistic Hamiltoniansystem are obtained. Two examples are given to illustrate the application of the results. 相似文献
17.
LUOShao-Kai 《理论物理通讯》2003,40(2):133-136
For a relativistic Birkhoflan system, the first integrals and the construction of integral invariants are studied. Firstly, the cyclic integrals and the generalized energy integral of the system are found by using the perfect differential method. Secondly, the equations of nonsimultaneous variation of the system are established by using the relation between the simultaneous variation and the nonsimultaneous variation. Thirdly, the relation between the first integral and the integral invariant of the system is studied, and it is proved that, using a t~rst integral, we can construct an integral invarlant of the system. Finally, the relation between the relativistic Birkhoflan dynamics and the relativistic Hamilton;an dynamics is discussed, and the first integrals and the integral invariants of the relativistic Hamiltonian system are obtained. Two examples are given to illustrate the application of the results. 相似文献
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19.
研究Birkhoff系统的约化.首先,列出系统的运动微分方程及其循环积分;其次,构造Birkhoff系统的Routh函数组,利用循环积分约化Birkhoff系统的运动微分方程,并使约化后的动力学方程仍保持Birkhoff方程的形式;最后,举例说明结果的应用.
关键词:
Birkhoff系统
约化
循环积分 相似文献
20.
Jaume Llibre 《Physics letters. A》2011,375(7):1080-1083
We study the limit cycles of a wide class of second order differential equations, which can be seen as a particular perturbation of the harmonic oscillator. In particular, by choosing adequately the perturbed function we show, using the averaging theory, that it is possible to obtain as many limit cycles as we want. 相似文献