共查询到20条相似文献,搜索用时 109 毫秒
1.
研究Chetaev型约束力学系统Appell方程的Lie对称性和Lie对称性直接导致的守恒量.分析Lagrange函数和A函数的关系;讨论Chetaev型约束力学系统Appell方程的Lie对称性导致的守恒量的一般研究方法;在群的无限小变换下,给出Appell方程Lie对称性的定义和判据;得到Lie对称性的结构方程以及Lie对称性直接导致的守恒量的表达式.举例说明结果的应用.
关键词:
Appell方程
Chetaev 型约束力学系统
Lie对称性
守恒量 相似文献
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由牛顿第二定律得到二维各向同性带电谐振子在均匀磁场中运动的运动微分方程,通过对运动微分方程的直接积分得到系统的两个积分(守恒量).利用Legendre变换建立守恒量与Lagrange函数间的关系,从而求得系统的Lagrange函数,并讨论与守恒量相应的无限小变换的Noether对称性与Lie对称性,最后求得系统的运动学方程. 相似文献
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利用代数方程和微分方程在无限小变换下的不变性,研究带有伺服约束的非完整系统的Lie 对称性.给出Lie对称性的确定方程、限制方程、结构方程,并给出守恒量的形式.
关键词:
非完整系统
伺服约束
Lie对称性
守恒量 相似文献
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从一维减幅-增幅谐振子的运动微分方程出发得到系统的运动积分常数,从而得到系统的Lagrange函数和Hamilton函数,再根据Hamilton函数的形式假定守恒量的形式,由Poisson括号的性质得到了系统的三个守恒量,并讨论与三个守恒量相应的无限小变换的Noether对称性与Lie对称性.还对守恒量与对称性的物理意义作了合理的解释.
关键词:
一维减幅-增幅谐振子
守恒量
Noether对称性
Lie对称性 相似文献
8.
采用变劲度系数的耦合弹簧构建一实际的两自由度弱非线性耦合系统, 用近似Lie对称性理论研究系统的一阶近似Lie对称性与近似守恒量, 得到6个一阶近似Lie对称性和一阶近似守恒量, 其中1个一阶近似守恒量实为系统的精确守恒量, 4个一阶近似守恒量为平凡的一阶近似守恒量, 只有1个一阶近似守恒量为稳定的一阶近似守恒量.
关键词:
两自由度弱非线性耦合系统
近似Lie对称性
近似守恒量 相似文献
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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
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We consider a Bianchi type I physical metric g, an auxiliary metric q and a density matter ρ in Eddington-inspired-Born-Infeld theory. We first derive a system of second order nonlinear ordinary differential equations. Then, by a suitable change of variables, we arrive at a system of first order nonlinear ordinary differential equations. Using both the solution-tube concept for the first order nonlinear ordinary differential equations and the nonlinear analysis tools such as the Arzelá–Ascoli theorem, we prove an existence result for the nonlinear system obtained. The resolution of this last system allows us to obtain new exact solutions for the model considered. Finally, by studying the asymptotic behaviour of the exact solutions obtained, we conclude that this solution is the counterpart of the Friedman–Lemaître–Robertson–Walker spacetime in Eddington-inspired-Born-Infeld theory. 相似文献
14.
L. A. Ferreira J. F. Gomes A. V. Razumov M. V. Saveliev A. H. Zimerman 《Communications in Mathematical Physics》1999,203(3):649-666
We associate to an arbitrary ℤ-gradation of the Lie algebra of a Lie group a system of Riccati-type first order differential
equations. The particular cases under consideration are the ordinary Riccati and the matrix Riccati equations. The multidimensional
extension of these equations is given. The generalisation of the associated Redheffer–Reid differential systems appears in
a natural way. The connection between the Toda systems and the Riccati-type equations in lower and higher dimensions is established.
Within this context the integrability problem for those equations is studied. As an illustration, some examples of the integrable
multidimensional Riccati-type equations related to the maximally nonabelian Toda systems are given.
Received: 3 August 1998 / Accepted: 21 December 1998 相似文献
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Andrzej Krasiński 《General Relativity and Gravitation》2001,33(1):145-161
The program Ortocartan for algebraic calculations in relativity has just been implemented in the Codemist Standard Lisp and can now be used under the Windows 98 and Linux operating systems. The paper describes the new facilities and subprograms that have been implemented since the previous release in 1992. These are: the possibility to write the output as Latex input code and as Ortocartan's input code, the calculation of the Ellis evolution equations for the kinematic tensors of flow, the calculation of the curvature tensors from given (torsion-free) connection coefficients in a manifold of arbitrary dimension, the calculation of the lagrangian from a given metric by the Landau-Lifshitz method, the calculation of the Euler–Lagrange equations from a given lagrangian (only for sets of ordinary differential equations) and the calculation of first integrals of sets of ordinary differential equations of second order (the first integrals are assumed to be polynomials of second degree in the first derivatives of the functions). 相似文献
16.
A new expansion method of first order nonlinear ordinary differential equation with at most a sixth-degree nonlinear term and its application to mBBM model 下载免费PDF全文
Based on a first order nonlinear ordinary differential equation with at most a sixth-degree nonlinear term which is extended from a type of elliptic equation, and by converting it into a new expansion form, this paper proposes a new algebraic method to construct exact solutions for nonlinear evolution equations. Being concise and straightforward, the method is applied to modified Benjamin-Bona-Mahony (mBBM) model, and some new exact solutions to the system are obtained. The algorithm is of important significance in exploring exact solutions for other nonlinear evolution equations. 相似文献
17.
Algebraic dynamics solutions and algebraic dynamics algorithm for nonlinear ordinary differential equations 总被引:2,自引:2,他引:0
The problem of preserving fidelity in numerical computation of nonlinear ordinary differential equations is studied in terms
of preserving local differential structure and approximating global integration structure of the dynamical system. The ordinary
differential equations are lifted to the corresponding partial differential equations in the framework of algebraic dynamics,
and a new algorithm—algebraic dynamics algorithm is proposed based on the exact analytical solutions of the ordinary differential
equations by the algebraic dynamics method. In the new algorithm, the time evolution of the ordinary differential system is
described locally by the time translation operator and globally by the time evolution operator. The exact analytical piece-like
solution of the ordinary differential equations is expressed in terms of Taylor series with a local convergent radius, and
its finite order truncation leads to the new numerical algorithm with a controllable precision better than Runge Kutta Algorithm
and Symplectic Geometric Algorithm. 相似文献
18.
外光场下电子与库仑势散射的schrodinger 方程可用Floque 分波法分离变量. 径向波动方程是一组无限祸合的二次线性微分方程组, 当弱外光场可视为微扰, 方程组将近似为二次常微分方程并且可积, 由此可得径向波函数、s 矩阵、截面. 无论何种极化或是否作偶极近似,共振谱线是普遍存在的, 井给出共振能量和强度的计算公式.
关键词: 相似文献
19.
Hong Yuan 《中国科学G辑(英文版)》2008,51(6):678-686
Based on the dynamic equations of nonlinear large deflection of axisymmetric shallow shells of revolution, the nonlinear free
vibration and forced vibration of a corrugated shallow shell under concentrated load acting at the center have been investigated.
The nonlinear partial differential equations of shallow shell were reduced to the nonlinear integral-differential equations
by using the method of Green’s function. To solve the integral-differential equations, the expansion method was used to obtain
Green’s function. Then the integral-differential equations were reduced to the form with a degenerate core by expanding Green’s
function as a series of characteristic function. Therefore, the integral-differential equations became nonlinear ordinary
differential equations with regard to time. The amplitude-frequency relation, with respect to the natural frequency of the
lowest order and the amplitude-frequency response under harmonic force, were obtained by considering single mode vibration.
As a numerical example, nonlinear free and forced vibration phenomena of shallow spherical shells with sinusoidal corrugation
were studied. The obtained solutions are available for reference to the design of corrugated shells. 相似文献
20.
《Journal of Nonlinear Mathematical Physics》2013,20(2):211-216
Abstract We present here the explicit parametric solutions of second order differential equations invariant under time translation and rescaling and third order differential equations invariant under time translation and the two homogeneity symmetries. The computation of first integrals gives in the most general case, the parametric form of the general solution. For some polynomial functions we obtain a time parametrisation quadrature which can be solved in terms of “known” functions. 相似文献