Dynamics of Multibody Systems Subjected to Impulsive Constraints

This paper presents a procedure for studying dynamics of multibodysystems subjected to impulsive constraints which may be either holonomicor nonholonomic. The procedure automatically incorporates the effects ofimpulsive constraints through its analysis. The governing equationsthemselves are developed from Kane's equations, using partial velocityvectors and partial angular velocity vectors. Explicit expressions forthe coefficients and terms of the governing equations are presented. Twosubcases are studied: (1) the constraints are instantaneously applied andcontinue to act; and (2) the constraints are instantaneously applied andlifted immediately after completion of impact. The internal impulses ateach joint and constraint impulses associated with the impulsiveconstraints are calculated. The procedure is checked with two examples,whose solutions are established.     

On the First-Order Decoupling of Dynamical Equations of Motion for Elastic Multibody Systems as Applied to a Two-Link Flexible Manipulator

An improved method for deriving elastic generalized coordinatesis considered. Then Kane's equations of motion for multibody systemsconsisting of an arbitrary number of rigid and elastic bodies ispresented. The equations are in general form and are applicable for anydesired holonomic system. Flexibility in choosing generalized speeds interms of generalized coordinate derivatives in Kane's method is used. Itis shown that proper choice of a congruency transformation betweengeneralized coordinate derivatives and generalized speeds leads toequations of motion for holonomic multibody systems consisting of anarbitrary number of rigid and elastic bodies. These equations aredecoupled in first-order terms. In order to show the use of this method,a simple system consisting of a lumped mass, a spring and a clamped-freeelastic beam is modeled. Finally, the numerical implementation ofdecoupling using congruency transformation is discussed and shown viasimulation of a two-degrees-of-freedom flexible robot.     

Principle of Dynamical Balance for Multibody Systems

A new formulation for multibody system dynamics is developed based on the concept of dynamical balance. In particular, we address the problem how to compose two known subsystem dynamics to generate the equations of motion for a composite system. The principle states that dynamical balance should hold between two subsystems, or the so-called d'Alembertian wrenches and torques of two subsystems should balance each other, for composite systems. The notion of body twists and wrenches is utilized to describe the principle. According to the principle, the dynamical balance condition is obtained just by taking the dual expression of the kinematical constraint in terms of the d'Alembertian wrenches and torques of subsystem dynamics. This work was supported by the Korea Research Foundation Grant (KRF-2003-003-D00015).     

On Derivation of Motion Equations for Systems with Non-Holonomic High-Order Program Constraints

The paper develops and discusses the generalization of modeling methods for systems with non-holonomic constraints. The classification of constraints has been revisited and a concept of program constraints introduced. High-order non-holonomic constraints (HONC), as presented in examples, are the generalization of the constraint concept and may, as a constraint class, include many of motion requirements that are put upon mechanical systems. Generalized program motion equations (GPME) that have been derived in the paper can be applied to systems with HONC. Concepts of virtual displacements and a generalized variational principle for high-order constraints are presented. Classical modeling methods for non-holonomic systems based on Lagrange equations with multipliers, Maggi, Appell–Gibbs, Boltzman–Hamel, Chaplygin and others are peculiar cases of GPME. The theory has been illustrated with examples of high-order constraints. Motion equations have been derived for a system subjected to a constraint that programmed a trajectory curvature profile. Efficiency, advantages and disadvantages of GPME have been discussed.     

An Implicit Multistage Integration Method Including Projection for the Numerical Simulation of Constrained Multibody Systems

To be efficient, the simulation of multibody system dynamics requires fast and robust numerical algorithms for the time integration of the motion equations usually described by Differential Algebraic Equations (DAEs). Firstly, multistep schemes especially built up for second-order differential equations are developed. Some of them exhibit superior accuracy and stability properties than standard schemes for first-order equations. However, if unconditional stability is required, one must be satisfied with second-order accurate methods, like one-step schemes from the Newmark family.Multistage methods for which high accuracy is not contradictory with stringent stability requirements are then addressed. More precisely, a two-stage, third-order accurate Implicit Runge–Kutta (IRK) method which possesses the desirable properties of unconditional stability combined with high-frequency dissipation is proposed.Projection methods which correct the integrated estimates of positions, velocities and accelerations are suggested to keep the constraint equations satisfied during the numerical integration. The resulting time integration algorithm can be easily implemented in existing incremental/iterative codes. Numerical results indicate that this approach compares favourably with classical methods.     

On the Equations of Kinematics and Dynamics of Constrained Mechanical Systems

The method of constructing of kinematical and dynamicalequations of mechanical systems, applied to numerical realization, isproposed in this paper. The corresponding difference equations, whichare obtained, give a guarantee of computations with given precision. Theequations of programmed constraints and those of constraintperturbations are defined. The stability of the programmed manifold fornumerical solutions of the kinematical and dynamical equations isobtained by means of corresponding construction of the constraintperturbation equations. The dynamical equations of system withprogrammed constraints are set up in the form of Lagrange equations ingeneralized coordinates. Certain inverse problems of rigid body dynamicsare considered.     

Dynamics of Flexible Multibody Systems with Non-Holonomic Constraints: A Finite Element Approach

In this article it is shown how non-holonomic constraints can beincluded in the formulation of the dynamic equations of flexiblemultibody systems. The equations are given in state space formwith the degrees of freedom, their derivatives and the kinematiccoordinates as state variables, which circumvents the use ofLagrangian multipliers. With these independent state variables forthe system the derivation of the linearized equations of motion isstraightforward. The incorporation of the method in a finiteelement based program for flexible multibody systems is discussed.The method is illustrated by three examples, which show, amongother things, how the linearized equations can be used to analysethe stability of a nominal steady motion.     

基于混合遗传算法求解非线性方程组

将非线性方程组的求解问题转化为函数优化问题,且综合考虑了拟牛顿法和遗传算法各自的优点,提出了一种用于求解非线性方程组的混合遗传算法。该混合算法充分发挥了拟牛顿法的局部搜索、收敛速度快和遗传算法的群体搜索、全局收敛的优点。为了证明该混合遗传算法的有效性,选择了几个典型的非线性方程组,从实验计算结果、收敛可靠性指标对比不同算法进行分析。数值模拟实验表明,该混合遗传算法具有很高的精确性和收敛性,是求解非线性方程组的一种有效算法。     

求解非线性方程组的量子行为粒子群算法

介绍了利用量子行为粒子群算法解决非线性方程组的问题.求方程组的解归结为一个最优化问题,当方程组有多个解时,它的适应值函数就是具有多个最优解的多峰函数.为此,引进一种物种形成原理算法,该算法根据群体微粒的相似度并行地分成子群体.每个子群体是围绕一个群体种子而建立的.对每个子群体进行QPSO最优搜索,从而保证方程组中每个可能的解都能被搜索到,具有良好的局部寻优特性.对几个重要的测试函数进行仿真实验,结果证明了所用算法可以保证找到方程组所有的解,并且具有很好的精确度.     

An Optimized Iterative Method for Numerical Solution of Large Systems of Equations Based on the Extremal Property of Zeroes of Chebyshev Polynomials

An iterative method suitable for numerical solution of large systems of equations is presented. An extremal property of the Chebyshev polynomials is established, providing a logical foundation for the proposed procedure. A modification of the method is applicable for evaluation of the maximal eigenvalue of a matrix with real eigenvalues and of the associated eigenvector.     

A Method for Solution of Systems of Linear Algebraic Equations with m-Dimensional @lambda;-Matrices

A system of linear algebraic equations with m-dimensional @lambda;-matrices is considered. The proposed method of searching for the solution of this system lies in reducing it to a numerical system of a special kind.     

Algorithmic Foundations of Creation of an Intelligent Software Tool for Investigation and Solution of Cauchy Problems for Systems of Ordinary Differential Equations

Methods are proposed for computer investigation of properties of systems of ordinary differential equations. Based on these methods, algorithms are created for computation of the value of the integration step that provides the stability of a numerical method and obtaining its results with a preassigned accuracy. The components and modes of operation of an intelligent software tool supporting the proposed methods are presented.     

Obstructions to the Existence of Universal Stabilizers for Smooth Control Systems

This paper states necessary conditions for the existence of universal stabilizers for smooth control systems. Roughly speaking, given a control system and a set {\cal U} of reference input functions, by universal stabilizer we mean a continuous feedback law that stabilizes the state of the system asymptotically to any of the reference trajectories produced by (arbitrary) inputs in {\cal U}. For an example, consider Brocketts nonholonomic integrator, with {\cal U} representing a set of uniformly bounded, piecewise continuous functions of time. This systems state can be asymptotically stabilized to any reference trajectory provided the latter is persistently exciting (PE). By contrast, for constant trajectories (i.e., equilibria), which are not PE, asymptotic stabilization is impossible by means of continuous pure-state feedback, in view of Brocketts obstruction. However, since this obstruction can be circumvented by the use of time-varying state feedback, one might reasonably expect to be able to design a (time-varying) continuous control law capable of asymptotically stabilizing the state to arbitrary reference trajectories, be they PE or not. Surprisingly, a consequence of the results in this paper is that, for systems with nonholonomic constraints frequently found in control applications, if {\cal U} contains reference functions that are not PE, then the universal stabilization problem cannot be solved, even if time-varying feedback is used. Date received: December 7, 2002. Date revised: June 30, 2003. Part of this work was conducted at INRIA Sophia-Antipolis, France, while the author completed his doctoral work with financial support from CONACYT, México.