|
Contact Dynamics
Contact dynamics deals with the motion of multibody systems subjected to unilateral contacts and friction. Such systems are omnipresent in many multibody dynamics applications. Consider for example * Contacts between wheels and ground in vehicle dynamics * Squealing of brakes due to friction induced oscillations * Motion of many particles, spheres which fall in a funnel, mixing processes (granular media) * Clockworks * Walking machines * Arbitrary machines with limit stops, friction. *Anatomic tissues (skin, iris/lens, eyelids/anterior ocular surface, joint cartilages, vascular endothelium/blood cells, muscles/tendons, et cetera) In the following it is discussed how such mechanical systems with unilateral contacts and friction can be modeled and how the time evolution of such systems can be obtained by numerical integration. In addition, some examples are given. Modeling The two main approaches for modeling mechanical systems with unilateral contacts and friction are the regulariz ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multibody System
Multibody system is the study of the dynamics (physics), dynamic behavior of interconnected rigid body, rigid or flexible body, flexible bodies, each of which may undergo large Translation (physics), translational and rotational displacements. Introduction The systematic treatment of the dynamic behavior of interconnected bodies has led to a large number of important multibody formalisms in the field of mechanics. The simplest bodies or elements of a multibody system were treated by Isaac Newton, Newton (free particle) and Leonhard Euler, Euler (rigid body). Euler introduced reaction forces between bodies. Later, a series of formalisms were derived, only to mention Joseph Louis Lagrange, Lagrange’s formalisms based on minimal coordinates and a second formulation that introduces constraints. Basically, the motion of bodies is described by their kinematic behavior. The Analytical dynamics, dynamic behavior results from the equilibrium of applied forces and the rate of change of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linear Complementarity Problem
In mathematical optimization theory, the linear complementarity problem (LCP) arises frequently in computational mechanics and encompasses the well-known quadratic programming as a special case. It was proposed by Cottle and Dantzig in 1968. Formulation Given a real matrix ''M'' and vector ''q'', the linear complementarity problem LCP(''q'', ''M'') seeks vectors ''z'' and ''w'' which satisfy the following constraints: * w, z \geqslant 0, (that is, each component of these two vectors is non-negative) * z^Tw = 0 or equivalently \sum\nolimits_i w_i z_i = 0. This is the complementarity condition, since it implies that, for all i, at most one of w_i and z_i can be positive. * w = Mz + q A sufficient condition for existence and uniqueness of a solution to this problem is that ''M'' be symmetric positive-definite. If ''M'' is such that has a solution for every ''q'', then ''M'' is a Q-matrix. If ''M'' is such that have a unique solution for every ''q'', then ''M'' is a P ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Contact Mechanics
Contact mechanics is the study of the Deformation (mechanics), deformation of solids that touch each other at one or more points. A central distinction in contact mechanics is between Stress (mechanics), stresses acting perpendicular to the contacting bodies' surfaces (known as normal stress) and frictional stresses acting Tangential and normal components, tangentially between the surfaces (shear stress). Normal contact mechanics or frictionless contact mechanics focuses on normal stresses caused by applied normal forces and by the adhesion present on surfaces in close contact, even if they are clean and dry. ''Frictional contact mechanics'' emphasizes the effect of friction forces. Contact mechanics is part of mechanical engineering. The physical and mathematical formulation of the subject is built upon the mechanics of materials and continuum mechanics and focuses on computations involving Elasticity (physics), elastic, viscoelasticity, viscoelastic, and Plastic Deformation, p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multibody System
Multibody system is the study of the dynamics (physics), dynamic behavior of interconnected rigid body, rigid or flexible body, flexible bodies, each of which may undergo large Translation (physics), translational and rotational displacements. Introduction The systematic treatment of the dynamic behavior of interconnected bodies has led to a large number of important multibody formalisms in the field of mechanics. The simplest bodies or elements of a multibody system were treated by Isaac Newton, Newton (free particle) and Leonhard Euler, Euler (rigid body). Euler introduced reaction forces between bodies. Later, a series of formalisms were derived, only to mention Joseph Louis Lagrange, Lagrange’s formalisms based on minimal coordinates and a second formulation that introduces constraints. Basically, the motion of bodies is described by their kinematic behavior. The Analytical dynamics, dynamic behavior results from the equilibrium of applied forces and the rate of change of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Contact Dynamics Woodpecker
Contact may refer to: Interaction Physical interaction * Contact (geology), a common geological feature * Contact lens or contact, a lens placed on the eye * Contact sport, a sport in which players make contact with other players or objects * Contact juggling * Contact mechanics, the study of solid objects that deform when touching each other * Contact process (mathematics), a model of an interacting particle system * Electrical contacts * ''Sparśa'', a concept in Buddhism that in Sanskrit/Indian language is translated as "contact", "touching", "sensation", "sense impression", etc. Social interaction * Contact (amateur radio) * Contact (law), a concept related to visitation rights * Contact (social), a person who can offer help in achieving goals * Contact Conference, an annual scientific conference * Extraterrestrial contact, see Search for extraterrestrial intelligence * First contact (anthropology), an initial meeting of two cultures * Language contact, the interaction of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Differential Algebraic Equation
In mathematics, a differential-algebraic system of equations (DAE) is a system of equations that either contains differential equations and algebraic equations, or is equivalent to such a system. The set of the solutions of such a system is a ''differential algebraic variety'', and corresponds to an ideal in a differential algebra of differential polynomials. In the univariate case, a DAE in the variable ''t'' can be written as a single equation of the form :F(\dot x, x, t)=0, where x(t) is a vector of unknown functions and the overdot denotes the time derivative, i.e., \dot x = \frac. They are distinct from ordinary differential equation (ODE) in that a DAE is not completely solvable for the derivatives of all components of the function ''x'' because these may not all appear (i.e. some equations are algebraic); technically the distinction between an implicit ODE system hat may be rendered explicitand a DAE system is that the Jacobian matrix \frac is a singular matrix ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gauss–Seidel Method
In numerical linear algebra, the Gauss–Seidel method, also known as the Liebmann method or the method of successive displacement, is an iterative method used to solve a system of linear equations. It is named after the German mathematicians Carl Friedrich Gauss and Philipp Ludwig von Seidel. Though it can be applied to any matrix with non-zero elements on the diagonals, convergence is only guaranteed if the matrix is either strictly diagonally dominant, or symmetric and positive definite. It was only mentioned in a private letter from Gauss to his student Gerling in 1823. A publication was not delivered before 1874 by Seidel. Description Let \mathbf A\mathbf x = \mathbf b be a square system of linear equations, where: \mathbf A = \begin a_ & a_ & \cdots & a_ \\ a_ & a_ & \cdots & a_ \\ \vdots & \vdots & \ddots & \vdots \\a_ & a_ & \cdots & a_ \end, \qquad \mathbf = \begin x_ \\ x_2 \\ \vdots \\ x_n \end , \qquad \mathbf = \begin b_ \\ b_2 \\ \vdots \\ b_n \end. When ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jacobi Method
In numerical linear algebra, the Jacobi method (a.k.a. the Jacobi iteration method) is an iterative algorithm for determining the solutions of a strictly diagonally dominant system of linear equations. Each diagonal element is solved for, and an approximate value is plugged in. The process is then iterated until it converges. This algorithm is a stripped-down version of the Jacobi transformation method of matrix diagonalization. The method is named after Carl Gustav Jacob Jacobi. Description Let A\mathbf x = \mathbf b be a square system of ''n'' linear equations, where:A = \begin a_ & a_ & \cdots & a_ \\ a_ & a_ & \cdots & a_ \\ \vdots & \vdots & \ddots & \vdots \\a_ & a_ & \cdots & a_ \end, \qquad \mathbf = \begin x_ \\ x_2 \\ \vdots \\ x_n \end , \qquad \mathbf = \begin b_ \\ b_2 \\ \vdots \\ b_n \end. When A and \mathbf b are known, and \mathbf x is unknown, we can use the Jacobi method to approximate \mathbf x. The vector \mathbf x^ denotes our initial guess for \mat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
