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1.
和Hamilton-Jacobi方法类似,Vujanovi?场方法把求解常微分方程组特解的问题转化为寻找一个一阶拟线性偏微分方程(基本偏微分方程)完全解的问题,但Vujanovi?场方法依赖于求出基本偏微分方程的完全解,而这通常是困难的,这就极大地限制了场方法的应用.本文将求解常微分方程组特解的Vujanovi?场方法改进为寻找动力学系统运动方程第一积分的场方法,并将这种方法应用于一阶线性非完整约束系统Riemann-Cartan位形空间运动方程的积分问题中.改进后的场方法指出,只要找到基本偏微分方程的包含m(m≤ n,n为基本偏微分方程中自变量的数目)个任意常数的解,就可以由此找到系统m个第一积分.特殊情况下,如果能够求出基本偏微分方程的完全解(完全解是m=n时的特例),那么就可以由此找到≤系统全部第一积分,从而完全确定系统的运动.Vujanovi?场方法等价于这种特殊情况. 相似文献
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We present a new methodology for studying the mean-square exponential stability and instability of nonlinear nonholonomic systems under disturbance of Gaussian white-noise by the first approximation. Firstly, we give the linearized equations of nonlinear nonholonomic stochastic systems; then we construct a proper stochastic Lyapunov function to investigate the mean-square exponential stability and instability of the linearized systems, and thus determine the stability and instability in probability of corresponding competing systems. An example is given to illustrate the application procedures. 相似文献
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Potential method of integration for solving the equations of mechanical systems 总被引:1,自引:0,他引:1 下载免费PDF全文
This paper is intended to apply a potential method of integration
to solving
the equations of holonomic and nonholonomic systems. For a holonomic
system, the differential
equations of motion can be written as a system of differential equations
of first order and its fundamental partial
differential equation is solved by using the potential method of
integration. For a nonholonomic system,
the equations of the corresponding holonomic system are solved by using
the method and then the restriction of
the nonholonomic constraints on the initial conditions of motion is
added. 相似文献
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利用一类周期性变系数线性常微分方程解的基本矩阵的Jordan形,分析一类非线性相对转动系统扭转的运动稳定性,从而得到非线性相对转动周期系统的运动稳定准则. 运用Lyapunov函数法,对广泛存在的一类机械传动系统的相对转动运动的平衡稳定位置的稳定域进行研究,并给出数学解析表达式. 这为工程中广泛存在的这类机械传动系统稳定工作区间工作参数的选取和相似模拟提供了理论依据及方法,据此可进一步分析和评价大型复杂旋转机械主传动系统的扭振稳定性.
关键词:
相对转动
相似模拟
运动稳定
平衡稳定 相似文献
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研究El-Nabulsi动力学模型下非Chetaev型非完整系统精确不变量与绝热不变量问题. 首先, 导出El-Nabulsi-d'Alembert-Lagrange原理并建立系统的运动微分方程. 其次, 建立El-Nabulsi模型下未受扰动的非Chetaev 型非完整系统的Noether对称性与Noether对称性导致的精确不变量之间的关系; 再次, 引入力学系统的绝热不变量概念, 研究受小扰动作用下非Chetaev型非完整系统Noether对称性的摄动导致绝热不变量问题, 给出了绝热不变量存在的条件及其形式. 作为特例, 本文讨论了El-Nabulsi模型下Chetaev型非完整系统的精确不变量与绝热不变量问题. 最后分别给出非Chetaev型和Chetaev型两种约束下的算例以说明结果的应用. 相似文献
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This paper investigates structure equation and Mei conserved quantity
of Mei symmetry of Appell equations for non-Chetaev nonholonomic
systems. Appell equations and differential equations of motion for
non-Chetaev nonholonomic mechanical systems are established. A new
expression of the total derivative of the function with respect to
time $t$ along the trajectory of a curve of the system is obtained,
the definition and the criterion of Mei symmetry of Appell equations
under the infinitesimal transformations of groups are also given. The
expressions of the structure equation and the Mei conserved quantity
of Mei symmetry in the Appell function are obtained. An example is
given to illustrate the application of the results. 相似文献
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This paper investigates structure equation and Mei conserved quantity of Mei symmetry of Appell equations for non-Chetaev nonholonomic systems. Appell equations and differential equations of motion for non-Chetaev nonholonomic mechanical systems are established. A new expression of the total derivative of the function with respect to time t along the trajectory of a curve of the system is obtained, the definition and the criterion of Mei symmetry of Appell equations under the infinitesimal transformations of groups are also given. The expressions of the structure equation and the Mei conserved quantity of Mei symmetry in the Appell function are obtained. An example is given to illustrate the application of the results. 相似文献
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Constraints are found on the spatial variation of finite-time Lyapunov exponents of two- and three-dimensional systems of ordinary differential equations. In a chaotic system, finite-time Lyapunov exponents describe the average rate of separation, along characteristic directions, of neighboring trajectories. The solution of the equations is a coordinate transformation that takes initial conditions (the Lagrangian coordinates) to the state of the system at a later time (the Eulerian coordinates). This coordinate transformation naturally defines a metric tensor, from which the Lyapunov exponents and characteristic directions are obtained. By requiring that the Riemann curvature tensor vanish for the metric tensor (a basic result of differential geometry in a flat space), differential constraints relating the finite-time Lyapunov exponents to the characteristic directions are derived. These constraints are realized with exponential accuracy in time. A consequence of the relations is that the finite-time Lyapunov exponents are locally small in regions where the curvature of the stable manifold is large, which has implications for the efficiency of chaotic mixing in the advection-diffusion equation. The constraints also modify previous estimates of the asymptotic growth rates of quantities in the dynamo problem, such as the magnitude of the induced current. (c) 2001 American Institute of Physics. 相似文献
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多无人机协同系统的过度扩散会引起协同失效, 对系统进行规模控制是解决该问题的一种潜在方法. 首先抽象出多无人机协同搜索系统的宏观运动特征, 进而建立平台的运动方程, 然后通过构造合适的李雅普诺夫函数, 获得该系统的稳定控制规律及其控制参数. 仿真结果表明: 1)本文所提的稳定控制机制不仅能够使多无人机系统实现有效的协同, 还能确保系统的稳定性; 2)在系统稳定时, 通过调整相关控制参数可以有效地控制系统规模.
关键词:
无人机
协同系统
稳定控制 相似文献
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建立具有一般非线性弹性力、广义摩阻力和谐波激励的一类相对转动非线性动力系统的动力学方程. 对相对转动非线性自治系统进行定性分析,通过构造Lyapunov函数研究自治系统奇点的稳定性. 运用多尺度法求解谐波激励下非自治系统在几种不同共振响应下的近似解,同时分析了主振系统稳态运动的稳定性.
关键词:
相对转动
非线性动力系统
Lyapunov函数
稳定性 相似文献
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The generalized variational principle of Herglotz type provides a variational method for describing nonconservative or dissipative processes. The purpose of this letter is to extend this variational principle to a first order linear nonholonomic system and study the conservation laws of the nonconservative nonholonomic system based on Herglotz variational problem. A new differential variational principle of the nonconservative nonholonomic system is proposed, which is based on Herglotz variational problem. And the differential equations of motion of the system are also obtained. Then, according to the condition for the invariance of the differential variational principle, the conservation theorem based on Herglotz variational problem for the nonconservative nonholonomic system are obtained. The theorem contains the conservation theorem of the nonconservative holonomic system as its special case, which can be reduced to the first Noether's theorem based on Herglotz variational problem under proper conditions. The inverse theorem of the conservation theorem is also provided and proved. An example is given to illustrate the application at the end of this letter. 相似文献
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Grégory Faye 《Physica D: Nonlinear Phenomena》2010,239(9):561-578
In this paper we study neural field models with delays which define a useful framework for modeling macroscopic parts of the cortex involving several populations of neurons. Nonlinear delayed integro-differential equations describe the spatio-temporal behavior of these fields. Using methods from the theory of delay differential equations, we show the existence and uniqueness of a solution of these equations. A Lyapunov analysis gives us sufficient conditions for the solutions to be asymptotically stable. We also present a fairly detailed study of the numerical computation of these solutions. This is, to our knowledge, the first time that a serious analysis of the problem of the existence and uniqueness of a solution of these equations has been performed. Another original contribution of ours is the definition of a Lyapunov functional and the result of stability it implies. We illustrate our numerical schemes on a variety of examples that are relevant to modeling in neuroscience. 相似文献
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Cooperative impulsive formation control for networked uncertain Euler–Lagrange systems with communication delays 下载免费PDF全文
This paper investigates the cooperative formation problem via impulsive control for a class of networked Euler–Lagrange systems. To reduce the energy consumption and communication frequency, the impulsive control method and cooperative formation control approach are combined. With the consideration of system uncertainties and communication delays among agents, neural networks-based adaptive technique is used for the controller design. Firstly, under the constraint that each agent interacts with its neighbors only at some sampling moments, an adaptive neural-networks impulsive formation control algorithm is proposed for the networked uncertain Euler–Lagrange systems without communication delays. Using Lyapunov stability theory and Laplacian potential function in the graph theory, we conclude that the formation can be achieved by properly choosing the constant control gains. Further, when considering communication delays,a modified impulsive formation control algorithm is proposed, in which the extended Halanay differential inequality is used to analyze the stability of the impulsive delayed dynamical systems. Finally, numerical examples and performance comparisons with continuous algorithm are provided to illustrate the effectiveness of the proposed methods. 相似文献
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In this Letter we consider modified function projective synchronization of unidirectionally coupled multiple time-delayed Rossler chaotic systems using adaptive controls. Recently, delay differential equations have attracted much attention in the field of nonlinear dynamics. The high complexity of the multiple time-delayed systems can provide a new architecture for enhancing message security in chaos based encryption systems. Adaptive control can be used for synchronization when the parameters of the system are unknown. Based on Lyapunov stability theory, the adaptive control law and the parameter update law are derived to make the state of two chaotic systems are function projective synchronized. Numerical simulations are presented to demonstrate the effectiveness of the proposed adaptive controllers. 相似文献
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We study a solution with an internal transition layer of a one-dimensional boundary value problem for the stationary reaction–advection–diffusion differential equation that arises in mathematical modeling of transport phenomena in the surface layer of the atmosphere in the case of non-uniform vegetation on the assumption of space isotropy along one of the horizontal axes and neutral atmospheric stratification. The parameters of the model at which a boundary value problem has a stable stationary solution with an internal transition layer localized near the boundary between different vegetation types are provided. The existence of such a solution and its local Lyapunov stability and uniqueness are proven. The results can be used for developing multidimensional substance transfer models in the case of a spatial heterogeneity. 相似文献