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1.
分析结构力学与有限元   总被引:24,自引:8,他引:16       下载免费PDF全文
分析力学历来是在动力学范围内论述的,结构力学与最优控制模拟关系的共同基础就是分析力学.这表明在结构力学与最优控制理论的架构内也应有分析力学的整套理论.本文就结构力学讲述分析力学,称分析结构力学.保守体系可用Hamilton体系的方法描述,其特点是保辛.保辛给出保守体系结构最重要的特性.有限元法是从结构力学发展的,有限元的单元刚度阵应保持对称性,其实这就是保辛.根据区段单元变形能只与其两端位移有关,就可通过数学分析得到Lagrange括号与Poisson括号,展示了其辛对偶体系、正则方程、正则变换等的内容.  相似文献
2.
As generalization of the fractional Fourier transform (FRFT), the linear canonical transform (LCT) has been used in several areas, including optics and signal processing. Many properties for this transform are already known, but the convolution theorems, similar to the version of the Fourier transform, are still to be determined. In this paper, the authors derive the convolution theorems for the LCT, and explore the sampling theorem and multiplicative filter for the band limited signal in the linear canonical domain. Finally, the sampling and reconstruction formulas are deduced, together with the construction methodology for the above mentioned multiplicative filter in the time domain based on fast Fourier transform (FFT), which has much lower computational load than the construction method in the linear canonical domain.  相似文献
3.
Energy-momentum conserving integration of multibody dynamics   总被引:1,自引:0,他引:1  
A rotationless formulation of multibody dynamics is presented, which is especially beneficial to the design of energy-momentum conserving integration schemes. The proposed approach facilitates the stable numerical integration of the differential algebraic equations governing the motion of both open-loop and closed-loop multibody systems. A coordinate augmentation technique for the incorporation of rotational degrees of freedom and associated torques is newly proposed. Subsequent to the discretization, size-reductions are performed to lower the computational costs and improve the numerical conditioning. In this connection, a new approach to the systematic design of discrete null space matrices for closed-loop systems is presented. Two numerical examples are given to evaluate the numerical properties of the proposed algorithms.  相似文献
4.
A DAE Approach to Flexible Multibody Dynamics   总被引:1,自引:0,他引:1  
The present work deals with the dynamics of multibody systems consisting ofrigid bodies and beams. Nonlinear finite element methods are used to devise a frame-indifferent spacediscretization of the underlying geometrically exact beam theory. Both rigid bodies and semi-discrete beams are viewed as finite-dimensional dynamical systems with holonomic constraints. The equations of motion pertaining to the constrained mechanical systems under considerationtake the form of Differential Algebraic Equations (DAEs).The DAEs are discretized directly by applying a Galerkin-based method.It is shown that the proposed DAE approach provides a unified framework for the integration of flexible multibody dynamics.  相似文献
5.
控制系统的哈密顿实现   总被引:1,自引:0,他引:1       下载免费PDF全文
考虑了非线性系统的反馈哈密顿实现问题,主要讨论两类系统:平面系统和输入通 道由拉格朗日子空间张成的系统.得到了一些公式和一个一般性的结果,该结果在某些情形 下变为更直接可验证条件.  相似文献
6.
This paper outlines results recently obtained in the problem of determining when an input-output map has a Hamiltonian realization. The results are obtained in terms of variations of the system trajectories, as in the solution of the Inverse Problem in Classical Mechanics. The variational and adjoint systems are introduced for any given nonlinear system, and self-adjointness defined. Under appropriate conditions self-adjointness characterizes Hamiltonian systems. A further characterization is given directly in terms of variations in the input and output trajectories, proving an earlier conjecture by the first author.  相似文献
7.
In this note we delve some more into the formal analogy of quantum mechanics and filtering theory, and we integrate the DMZ equation by transforming it into a Schroedinger equation that can be integrated in the standard way.  相似文献
8.
文中提出了Datalog程序的正规变换,并构造了Datalog程序的约束模型图,从而把正规变换的求解转化为对约束模式图的搜索。约束模式图搜索算法与经典的AO^*搜索算法及相关文献中的算法相比具有更高的效率。  相似文献
9.
The program LINA01 is proposed for the direct and the inverse normalization of Hamiltonian systems and for the calculation of formal integrals of motion of them. The calculations required in LINA01 are made on the basis of Lie canonical transformation method. The program package of LINA01 is written on REDUCE.

Program summary

Title of program:LINA01Catalogue identifier:ADUVProgram summary URL:http://cpc.cs.qub.ac.uk/summaries/ADUVProgram obtainable from:CPC Program Library, Queen's University of Belfast, N. IrelandComputer: IBM PC PENTIUM 4/2.40 GHz 512 MbOperating systems under which the program has been tested: Windows XPProgramming language used: REDUCE vs. 3.7No. of lines in distributed program, including test data, etc.:485No. of bytes in distributed program, including test data, etc.:4320Distribution format:tar.gz Nature of physical problem. The transformation bringing a given Hamiltonian function into the normal form (namely, the normalization) is one of the conventional methods for non-linear Hamiltonian systems [A.J. Lichtenberg, M.A. Lieberman, Regular and Stochastic Motion, Springer-Verlag, Berlin, 1983; G.D. Birkhoff, Dynamical Systems, A.M.S. Colloquium Publications, New York, 1927; F. Gustavson, Astron. J. 71 (1966) 670; G.I. Hori, Astron. Soc. Japan 18 (1966) 287; A. Deprit, Cel. Mech. 1 (1969) 12; A.A. Kamel, Cel. Mech. 3 (1970) 90]. Recently, beyond classical mechanics, the normal form method has been applied to quantization of chaotic Hamiltonian systems with the aim of finding quantum signature of chaos [L.E. Reichl, The Transition to Chaos. Conservative Classical Systems: Quantum Manifestations, Springer, New York, 1992]. Besides those utilities, the normalization requires quite cumbersome algebraic calculations of polynomials, so that the computer algebraic approach is worth studying to promote further investigations around the normalization together with the ones around the inverse normalization. Method of solution. The canonical transformation proceeding the normalization is expressed in terms of the Lie transformation power series, which is also referred to as the Hori-Deprit transformation. After (formal) power series expansion as above, the fundamental equation of the normalization is solved for the normal form together with the generating function of transformation recursively from degree-3 to the degree desired to be normalized. The generating function thus obtained is applied to the calculation of (formal) integrals of motion. Restrictions due to the complexity of the problem. The computation time rises in a combinatorial manner as the desired degree of normalization does. Especially, such a combinatorial growth of computation is more significant in the inverse normalization than in the direct one. The hardware (processor and memory, for example) available for the computation may restrict either the degree of normalization or the computation time.  相似文献
10.
The Serret-Andoyer transformation is a classical method for reducing the free rigid body dynamics, expressed in Eulerian coordinates, to a 2-dimensional Hamiltonian flow. First, we show that this transformation is the computation, in 3-1-3 Eulerian coordinates, of the symplectic (Marsden-Weinstein) reduction associated with the lifted left-action of SO(3) on T*SO(3)—a generalization and extension of Noether's theorem for Hamiltonian systems with symmetry. In fact, we go on to generalize the Serret-Andoyer transformation to the case of Hamiltonian systems on T*SO(3) with left-invariant, hyperregular Hamiltonian functions. Interpretations of the Serret-Andoyer variables, both as Eulerian coordinates and as canonical coordinates of the co-adjoint orbit, are given. Next, we apply the result obtained to the controlled rigid body with momentum wheels. For the class of Hamiltonian controls that preserve the symmetry on T*SO(3), the closed-loop motion of the main body can again be reduced to canonical form. This simplifies the stability proof for relative equilibria , which then amounts to verifying the classical Lagrange-Dirichlet criterion. Additionally, issues regarding numerical integration of closed-loop dynamics are also discussed. Part of this work has been presented in LumBloch:97a. This revised version was published online in July 2006 with corrections to the Cover Date.  相似文献
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