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1.
The generalized variational principle of Herglotz type provides an effective way to study the problems of conservative and non-conservative systems in a unified way. According to the differential variational principle of Herglotz type, we study the adiabatic invariants for a disturbed Birkhoffian system in this paper. Firstly, the differential equations of motion of the Birkhoffian system based upon this variational principle are given, and the exact invariant of Herglotz type of the system is introduced. Secondly, a new type of adiabatic invariants for the system under the action of small perturbation is obtained. Thirdly, the inverse theorem of adiabatic invariant for the disturbed Birkhoffian system of Herglotz type is obtained. Finally, an example is given. 相似文献
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The aim of this paper is to study the Herglotz variational principle of the fractional Birkhoffian system and its Noether symmetry and conserved quantities. First, the fractional Pfaff-Herglotz action and the fractional PfaffHerglotz principle are presented. Second, based on different definitions of fractional derivatives, four kinds of fractional Birkhoff's equations in terms of the Herglotz variational principle are established. Further, the definition and criterion of Noether symmetry of the fractional Birkhoffian system in terms of the Herglotz variational problem are given. According to the relationship between the symmetry and the conserved quantities, the Noether's theorems within four different fractional derivatives are derived, which can reduce to the Noether's theorem of the Birkhoffian system in terms of the Herglotz variational principle under the classical conditions. As applications of the Noether's t heorems of the fractional Birkhoffian system in terms of the Herglotz variational principle, an example is given at the end of this paper. 相似文献
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Conservation laws for the Birkhoffian system and the constrained Birkhoffian system of Herglotz type are studied. We propose a new differential variational principle, called the Pfaff-Birkhoff-d'Alembert principle of Herglotz type. Birkhoff's equations for both the Birkhoffian system and the constrained Birkhoffian system of Herglotz type are obtained. According to the relationship between the isochronal variation and the nonisochronal variation, the conditions of the invariance for the Pfaff-Birkhoff-d'Alembert principle of Herglotz type are given. Then, the conserved quantities for the Birkhoffian system and the constrained Birkhoffian system of Herglotz type are deduced. Furthermore, the inverse theorems of the conservation theorems are also established. 相似文献
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NOETHER'S THEOREM OF NONHOLONOMIC SYSTEMS OF NON-CHETAEV'S TYPE WITH UNILATERAL CONSTRAINTS 总被引:1,自引:0,他引:1 下载免费PDF全文
In this paper, we present Noether's theorem and its inverse theorem for nonholonomic systems of non-Chetaev's type with unilateral constraints. We present first the principle of Jourdain for the system and, on the basis of the invariance of the differential variational principle under the infinitesimal transformations of groups, we have established Noether's theory for the above systems. An example is given to illustrate the application of the result. 相似文献
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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 下载免费PDF全文
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
7.
We generalize Noether's theorem and the Poincaré invariant to conservative and nonconservative systems with nonlinear nonholonomic constraints. The conservation laws of such systems are illustrated. 相似文献
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In this paper we show that the first integrals of the discrete equation of motion for nonconservative and nonholonomic mechanical systems can be determined explicitly by investigating the invariance properties of the discrete Lagrangian. The result obtained is a discrete analogue of the generalized theorem of Noether in the Calculus of variations. 相似文献
9.
The methods of Ritz, Galerkin, and complementary energy are applied to a nonconservative problem in the theory of elastic stability. The numerical calculations are based upon (i) a variational expression, for which no functional can be determined, and (ii) an adjoint variational principle, for which a functional is established in terms of the variables of the original non-self-adjoint eigenvalue problem and the adjoint problem. The adjoint variational principle yields somewhat more accurate values for the critical load parameter than does the variational expression. In addition, the results obtained by means of the complementary energy method are more precise than the corresponding results obtained from the Ritz and Galerkin methods. 相似文献
10.
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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International Journal of Theoretical Physics - Herglotz variational principle, in which the functional is defined by a differential equation, generalizes the classical ones defining the functional... 相似文献
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Non-Noether symmetries and Lutzky conservative quantities of nonholonomic nonconservative dynamical systems 下载免费PDF全文
Non-Noether symmetries and conservative quantities of nonholonomic nonconservative dynamical systems are investigated in this paper. Based on the relationships among motion, nonconservative forces, nonholonomic constrained forces and Lagrangian, non-Noether symmetries and Lutzky conservative quantities are presented for nonholonomic nonconservative dynamical systems. The relation between non-Noether symmetry and Noether symmetry is discussed and it is further shown that non-Noether conservative quantities can be obtained by a complete set of Noether invariants. Finally,an example is given to illustrate these results. 相似文献
13.
In this letter, we investigate Noether symmetries and conservation laws of discrete dynamical systems on an uniform lattice with the nonholonomic constraints. Based on the quasi-invariance of discrete Hamiltonian action of the systems under the infinitesimal transformation with respect to the time and generalized coordinates, we give the discrete analogue of generalized variational formula of the systems. From this formula we derive the discrete analogue of generalized Noether-type identity, and then we present the generalized quasi-extremal equations of the systems. We also obtain the discrete analogue of Noether theorems and the discrete analogue of Noether conservation laws of the systems. Finally, an example is discussed to illustrate these results. 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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LUO En LIANG LiFu & LI WeiHua Department of Applied Mechanics Engineering Sun Yat-sen University Guangzhou China Department of Aerospace Engineering Harbin Engineering University Harbin China 《中国科学G辑(英文版)》2007,50(2):152-162
According to the basic idea of classical yin-yang complementarity and modern dual-complementarity, in a simple and unified new way proposed by Luo, the un-conventional Hamilton-type variational principles of holonomic conservative system in analytical mechanics can be established systematically. This unconventional Hamilton-type variational principle can fully characterize the initial-value problem of analytical mechanics, so that it is an important innovation for the Hamilton-type variational principle. In this paper, an important integral relation is given, which can be considered as the expression of the generalized principle of virtual work for analytical mechanics in mechanics. Based on this relation, it is possible not only to obtain the principle of virtual work of holonomic conservative system in analytical mechanics, but also to derive systematically the complementary functionals for three-field and two-field unconventional variational principles, and the functional for the one-field one by the generalized Legendre transformation given in this paper. Further, with this new approach, the intrinsic relationship among various principles can be explained clearly. Meanwhile, the unconventional Hamilton-type variational principles of nonholonomic conservative system in analytical mechanics can also be established systematically in this paper. 相似文献
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Lie symmetry and Mei conservation law of continuum Lagrange system are studied in this paper.The equation of motion of continuum system is established by using variational principle of continuous coordinates.The invariance of the equation of motion under an infinitesimal transformation group is determined to be Lie-symmetric.The condition of obtaining Mei conservation theorem from Lie symmetry is also presented.An example is discussed for applications of the results. 相似文献
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Integrating Factors and Conservation Theorems of Lagrangian Equations for Nonconservative Mechanical System in Generalized Classical Mechanics 总被引:1,自引:0,他引:1
QIAO Yong-Fen ZHAO Shu-Hong 《理论物理通讯》2006,46(1):43-45
The conservation theorems of the generalized Lagrangian equations for nonconservative mechanical system are studied by using method of integrating factors. Firstly, the differential equations of motion of system are given, and the definition of integrating factors is given. Next, the necessary conditions for the existence of the conserved quantity are studied in detail. Finally, the conservation theorem and its inverse for the system are established, and an example is given to illustrate the application of the result. 相似文献
19.
QIAO Yong-Fen ZHAO Shu-Hong 《理论物理通讯》2006,46(7)
The conservation theorems of the generalized Lagrangian equations for nonconservative mechanical system are studied by using method of integrating factors. Firstly, the differential equations of motion of system are given, and the definition of integrating factors is given. Next, the necessary conditions for the existence of the conserved quantity are studied in detail. Finally, the conservation theorem and its inverse for the system are established, and an example is given to illustrate the application of the result. 相似文献
20.
Momentum-dependent symmetries and non-Noether conserved quantities for nonholonomic nonconservative Hamilton canonical systems 下载免费PDF全文
This paper investigates the momentum-dependent symmetries for nonholonomic
nonconservative Hamilton canonical systems. The definition and determining
equations of the momentum-dependent symmetries are presented, based on the
invariance of differential equations under infinitesimal transformations
with respect to the generalized coordinates and generalized momentums. The
structure equation and the non-Noether conserved quantities of the systems
are obtained. The inverse issues associated with the momentum-dependent
symmetries are discussed. Finally, an example is discussed to further
illustrate the applications. 相似文献