Constraint Equations (constraint + equation)

Distribution by Scientific Domains


Selected Abstracts


The GDC method as an orthogonal arc-length method

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 4 2007
E. L. Cardoso
Abstract The method of generalized displacements (GDC) is a path-following algorithm for non-linear mechanics, capable to overcome both limit and snap-back points. It was proposed as a consistent alternative to most existing techniques, such as the arc-length family of algorithms. Although it is a reliable algorithm, it has not been as widely used as the arc-length methods, possibly because it has been seen as belonging to a different category. This paper shows that the GDC method can be seen as an orthogonal arc-length method, with an interesting constraint equation which leads to its appealing features. Copyright © 2006 John Wiley & Sons, Ltd. [source]


Adaptive output feedback tracking control of spacecraft formation

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 2-3 2002
Hong Wong
Abstract In this paper, an adaptive, output feedback control design methodology is presented for a spacecraft formation flying (SFF) system. A Lagrangian derivation of the SFF model is considered to produce position dynamics for follower spacecraft #n relative to follower spacecraft #(n,1), where n is an arbitrary positive integer, assuming that the leader spacecraft in the formation follows a no-thrust, natural, elliptical orbit. Next, a control law is designed to provide a filtered velocity measurement and a desired adaptive compensation with semi-global, asymptotic, relative position tracking. To show the efficacy of the control algorithm, all desired trajectories are generated online by numerically solving the unperturbed nonlinear SFF dynamics with initial conditions satisfying a no-thrust, natural orbit constraint equation. The proposed control law is simulated for the case of two and three spacecraft and is shown to yield semi-global, asymptotic tracking of the relative position in addition to the convergence of disturbance parameter estimates. Copyright © 2002 John Wiley & Sons, Ltd. [source]


Dynamics and Coupling Actuation of Elastic Underactuated Manipulators

JOURNAL OF FIELD ROBOTICS (FORMERLY JOURNAL OF ROBOTIC SYSTEMS), Issue 3 2003
Tie Shi Zhao
This paper investigates the constraint and coupling characteristics of underactuated manipulators by proposing an elastic model of the manipulator and examining the second order constraint equation. A dynamic model and a coupling constraint equation are developed from a Jacobian matrix and the Newton-Euler formulation. The inertia matrix and the Christoffel tensor are analyzed and decomposed into the part concerning actuated joints and the part concerning passive joints. This decomposition is further extended to the dynamic coupling equation and generates an actuation coupling matrix and a dynamic coupling tensor. Two new dynamic coupling indices are hence identified. One is related to an actuation input and the other is related to centrifugal and Coriolis forces. The former reveals the dynamic coupling between the input and the acceleration of passive joints and gives the actuation effect on the passive joints. The latter reveals the dynamic coupling between the centrifugal and Coriolis forces and the acceleration of passive joints and provides the centrifugal and Coriolis effect on the acceleration of passive joints. The study reveals the coupling characteristics of an underactuated manipulator. This is then demonstrated in a three-link manipulator and extended to a serial manipulator with passive prismatic joint. © 2003 Wiley Periodicals, Inc. [source]


Optimal transformations of asymmetric elements in three-phase networks

EUROPEAN TRANSACTIONS ON ELECTRICAL POWER, Issue 2 2005
Zdzislaw W. Trzaska
Abstract This paper presents a procedure for optimal transformation of asymmetric three-phase elements. The proposed algorithm is based on the solution of the corresponding Steiner problem and improves the network voltage and current profiles. After identifying the phase quantities, the problem is formulated as a non-linear programming problem of the minimization of the sum of the r.m.s. values of the phase voltages and line currents under some constraint equations. A few test networks are used to verify the effectiveness and accuracy of the method. It is believed that practical applications of the proposed method will enhance the estimation of the phase asymmetry of the three-phase generator voltages and load currents. Copyright © 2005 John Wiley & Sons, Ltd. [source]


Simulation of special loading conditions by means of non-linear constraints imposed through Lagrange multipliers

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 10 2002
M. A. Gutiérrez
Abstract This paper discusses the necessity and handling of non-linear constraint equations to describe the behaviour of properties of the loading system such as, e.g. smooth free-rotating loading platens. An exact, non-linear formulation for a smooth loading platen is derived and its incorporation into the equilibrium equations is presented. For this purpose, the Lagrange multiplier method is used. The solution of the equilibrium equations by means of a Newton,Raphson algorithm is also outlined. The proposed approach is validated on a patch of two finite elements and applied to a compression-bending test on a pre-notched specimen. It is observed that use of a linearized approximation of the boundary constraint can lead to errors in the description of the motion of the constrained nodes. Thus, the non-linear formulation is preferable. Copyright © 2002 John Wiley & Sons, Ltd. [source]


Imposition of essential boundary conditions by displacement constraint equations in meshless methods

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 3 2001
Xiong Zhang
Abstract One of major difficulties in the implementation of meshless methods is the imposition of essential boundary conditions as the approximations do not pass through the nodal parameter values. As a consequence, the imposition of essential boundary conditions in meshless methods is quite awkward. In this paper, a displacement constraint equations method (DCEM) is proposed for the imposition of the essential boundary conditions, in which the essential boundary conditions is treated as a constraint to the discrete equations obtained from the Galerkin methods. Instead of using the methods of Lagrange multipliers and the penalty method, a procedure is proposed in which unknowns are partitioned into two subvectors, one consisting of unknowns on boundary ,u, and one consisting of the remaining unknowns. A simplified displacement constraint equations method (SDCEM) is also proposed, which results in a efficient scheme with sufficient accuracy for the imposition of the essential boundary conditions in meshless methods. The present method results in a symmetric, positive and banded stiffness matrix. Numerical results show that the accuracy of the present method is higher than that of the modified variational principles. The present method is a exact method for imposing essential boundary conditions in meshless methods, and can be used in Galerkin-based meshless method, such as element-free Galerkin methods, reproducing kernel particle method, meshless local Petrov,Galerkin method. Copyright © 2001 John Wiley & Sons, Ltd. [source]


Discontinuous Galerkin framework for adaptive solution of parabolic problems

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2007
Deepak V. Kulkarni
Abstract Non-conforming meshes are frequently employed in adaptive analyses and simulations of multi-component systems. We develop a discontinuous Galerkin formulation for the discretization of parabolic problems that weakly enforces continuity across non-conforming mesh interfaces. A benefit of the DG scheme is that it does not introduce constraint equations and their resulting Lagrange multiplier fields as done in mixed and mortar methods. The salient features of the formulation are highlighted through an a priori analysis. When coupled with a mesh refinement scheme the DG formulation is able to accommodate multiple hanging nodes per element edge and leads to an effective adaptive framework for the analysis of interface evolution problems. We demonstrate our approach by analysing the Stefan problem of solidification. Copyright © 2006 John Wiley & Sons, Ltd. [source]


A tetrahedron approach for a unique closed-form solution of the forward kinematics of six-dof parallel mechanisms with multiconnected joints

JOURNAL OF FIELD ROBOTICS (FORMERLY JOURNAL OF ROBOTIC SYSTEMS), Issue 6 2002
Se-Kyong Song
This article presents a new formulation approach that uses tetrahedral geometry to determine a unique closed-form solution of the forward kinematics of six-dof parallel mechanisms with multiconnected joints. For six-dof parallel mechanisms that have been known to have eight solutions, the proposed formulation, called the Tetrahedron Approach, can find a unique closed-form solution of the forward kinematics using the three proposed Tetrahedron properties. While previous methods to solve the forward kinematics involve complicated algebraic manipulation of the matrix elements of the orientation of the moving platform, or closed-loop constraint equations between the moving and the base platforms, the Tetrahedron Approach piles up tetrahedrons sequentially to directly solve the forward kinematics. Hence, it allows significant abbreviation in the formulation and provides an easier systematic way of obtaining a unique closed-form solution. © 2002 Wiley Periodicals, Inc. [source]