|
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 regulari ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multibody System
Multibody system is the study of the dynamic behavior of interconnected rigid or flexible bodies, each of which may undergo large 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 Newton (free particle) and Euler (rigid body). Euler introduced reaction forces between bodies. Later, a series of formalisms were derived, only to mention 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 dynamic behavior results from the equilibrium of applied forces and the rate of change of momentum. Nowadays, the term multibody system is related to a large number of engineering fields of research, especially in robotics and vehi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quadratic Programming
Quadratic programming (QP) is the process of solving certain mathematical optimization problems involving quadratic functions. Specifically, one seeks to optimize (minimize or maximize) a multivariate quadratic function subject to linear constraints on the variables. Quadratic programming is a type of nonlinear programming. "Programming" in this context refers to a formal procedure for solving mathematical problems. This usage dates to the 1940s and is not specifically tied to the more recent notion of "computer programming." To avoid confusion, some practitioners prefer the term "optimization" — e.g., "quadratic optimization." Problem formulation The quadratic programming problem with variables and constraints can be formulated as follows. Given: * a real-valued, -dimensional vector , * an -dimensional real symmetric matrix , * an -dimensional real matrix , and * an -dimensional real vector , the objective of quadratic programming is to find an -dimensional vector , that wi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Siconos
SICONOS is an Open Source scientific software primarily targeted at modeling and simulating non-smooth dynamical systems (NSDS): * Mechanical systems (Rigid body or solid) with Unilateral contact and Coulomb friction as we find in Non-smooth mechanics, Contact dynamics or Granular material. * Switched Electrical Circuit such as Power converter, Rectifier, Phase-locked loop (PLL) or Analog-to-digital converter * Sliding mode control systems Other applications are found in Systems and Control (hybrid systems, differential inclusions, optimal control with state constraints), Optimization (Complementarity problem and Variational inequality) Biology Gene regulatory network, Fluid Mechanics and Computer graphics, etc. Components The software is based on 3 main components * Siconos/Numerics (C API). Collection of low-level algorithms for solving basic Algebra and optimization problems arising in the simulation of nonsmooth dynamical systems ** Linear complementarity problem (LCP) ** ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Contact Mechanics
Contact mechanics is the study of the deformation of solids that touch each other at one or more points.Johnson, K. L, 1985, Contact mechanics, Cambridge University Press.Popov, Valentin L., 2010, ''Contact Mechanics and Friction. Physical Principles and Applications'', Springer-Verlag, 362 p., . A central distinction in contact mechanics is between stresses acting perpendicular to the contacting bodies' surfaces (known as normal stress) and frictional stresses acting 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 fo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multibody System
Multibody system is the study of the dynamic behavior of interconnected rigid or flexible bodies, each of which may undergo large 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 Newton (free particle) and Euler (rigid body). Euler introduced reaction forces between bodies. Later, a series of formalisms were derived, only to mention 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 dynamic behavior results from the equilibrium of applied forces and the rate of change of momentum. Nowadays, the term multibody system is related to a large number of engineering fields of research, especially in robotics and vehi ... [...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 t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Contact Dynamics Motorbike
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 t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Contact Dynamics Billiard
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 t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Contact Dynamics Mixer
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 t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Differential Algebraic Equation
In electrical engineering, a differential-algebraic system of equations (DAEs) is a system of equations that either contains differential equations and algebraic equations, or is equivalent to such a system. In mathematics these are examples of ``differential algebraic varieties'' and correspond to ideals in differential polynomial rings (see the article on differential algebra for the algebraic setup. We can write these differential equations for a dependent vector of variables ''x'' in one independent variable ''t'', as ::F(\dot x(t),\, x(t),\,t)=0 When considering these symbols as functions of a real variable (as is the case in applications in electrical engineering or control theory) we look at x: ,bto\R^n as a vector of dependent variables x(t)=(x_1(t),\dots,x_n(t)) and the system has as many equations, which we consider as functions F=(F_1,\dots,F_n):\R^\to\R^n. They are distinct from ordinary differential equation (ODE) in that a DAE is not completely solvable for the deri ... [...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, and is similar to the Jacobi method. 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 The Gauss–Seidel method is an iterative technique for solving a square system of linear equations with unknown : A\mathbf x = \mathbf b . It is defined by the iteration L_* \mathbf^ = \mathbf - U \mathbf^, where \mathbf^ is the -th approximation or iteration of \mathbf,\,\mathbf^ is the next or -th it ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
