|
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] |
Unilateral Contact
In contact mechanics, the term unilateral contact, also called unilateral constraint, denotes a mechanical constraint which prevents penetration between two rigid/flexible bodies. Constraints of this kind are omnipresent in non-smooth multibody dynamics applications, such as granular flows, legged robot, vehicle dynamics, particle damping, imperfect joints, or rocket landings. In these applications, the unilateral constraints result in impacts happening, therefore requiring suitable methods to deal with such constraints. Modelling of the unilateral constraints There are mainly two kinds of methods to model the unilateral constraints. The first kind is based on smooth contact dynamics, including methods using Hertz's models, penalty methods, and some regularization force models, while the second kind is based on the non-smooth contact dynamics, which models the system with unilateral contacts as variational inequalities. Smooth contact dynamics In this method, normal force ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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] |
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-matrix ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Institut National De Recherche En Informatique Et En Automatique
The National Institute for Research in Digital Science and Technology (Inria) () is a French national research institution focusing on computer science and applied mathematics. It was created under the name ''Institut de recherche en informatique et en automatique'' (IRIA) in 1967 at Rocquencourt near Paris, part of Plan Calcul. Its first site was the historical premises of SHAPE (central command of NATO military forces), which is still used as Inria's main headquarters. In 1980, IRIA became INRIA. Since 2011, it has been styled ''Inria''. Inria is a Public Scientific and Technical Research Establishment (EPST) under the double supervision of the French Ministry of National Education, Advanced Instruction and Research and the Ministry of Economy, Finance and Industry. Administrative status Inria has 9 research centers distributed across France (in Bordeaux, Grenoble- Inovallée, Lille, Lyon, Nancy, Paris-Rocquencourt, Rennes, Saclay, and Sophia Antipolis) and one center ab ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Variational Inequality
In mathematics, a variational inequality is an inequality involving a functional, which has to be solved for all possible values of a given variable, belonging usually to a convex set. The mathematical theory of variational inequalities was initially developed to deal with equilibrium problems, precisely the Signorini problem: in that model problem, the functional involved was obtained as the first variation of the involved potential energy. Therefore, it has a variational origin, recalled by the name of the general abstract problem. The applicability of the theory has since been expanded to include problems from economics, finance, optimization and game theory. History The first problem involving a variational inequality was the Signorini problem, posed by Antonio Signorini in 1959 and solved by Gaetano Fichera in 1963, according to the references and : the first papers of the theory were and , . Later on, Guido Stampacchia proved his generalization to the Lax–Milgram the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Peer Reviewed
Peer review is the evaluation of work by one or more people with similar competencies as the producers of the work (peers). It functions as a form of self-regulation by qualified members of a profession within the relevant field. Peer review methods are used to maintain quality standards, improve performance, and provide credibility. In academia, scholarly peer review is often used to determine an academic paper's suitability for publication. Peer review can be categorized by the type of activity and by the field or profession in which the activity occurs, e.g., medical peer review. It can also be used as a teaching tool to help students improve writing assignments. Henry Oldenburg (1619–1677) was a German-born British philosopher who is seen as the 'father' of modern scientific peer review. Professional Professional peer review focuses on the performance of professionals, with a view to improving quality, upholding standards, or providing certification. In academia, peer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
SWIG
The Simplified Wrapper and Interface Generator (SWIG) is an open-source software tool used to connect computer programs or libraries written in C or C++ with scripting languages such as Lua, Perl, PHP, Python, R, Ruby, Tcl, and other languages like C#, Java, JavaScript, Go, D, OCaml, Octave, Scilab and Scheme. Output can also be in the form of XML. Function The aim is to allow the calling of native functions (that were written in C or C++) by other programming languages, passing complex data types to those functions, keeping memory from being inappropriately freed, inheriting object classes across languages, etc. The programmer writes an interface file containing a list of C/C++ functions to be made visible to an interpreter. SWIG will compile the interface file and generate code in regular C/C++ and the target programming language. SWIG will generate conversion code for functions with simple arguments; conversion code for complex types of arguments must be written by the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Impact (mechanics)
In mechanics, an impact is a high force or shock applied over a short time period when two or more bodies collide. Such a force or acceleration usually has a greater effect than a lower force applied over a proportionally longer period. The effect depends critically on the relative velocity of the bodies to one another. At normal speeds, during a perfectly inelastic collision, an object struck by a projectile will deform, and this deformation will absorb most or all of the force of the collision. Viewed from a conservation of energy perspective, the kinetic energy of the projectile is changed into heat and sound energy, as a result of the deformations and vibrations induced in the struck object. However, these deformations and vibrations cannot occur instantaneously. A high-velocity collision (an impact) does not provide sufficient time for these deformations and vibrations to occur. Thus, the struck material behaves as if it were more brittle than it would otherwise be, and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Newton–Euler Equations
In classical mechanics, the Newton–Euler equations describe the combined translational and rotational dynamics of a rigid body. Traditionally the Newton–Euler equations is the grouping together of Euler's two laws of motion for a rigid body into a single equation with 6 components, using column vectors and matrices. These laws relate the motion of the center of gravity of a rigid body with the sum of forces and torques (or synonymously moments) acting on the rigid body. Center of mass frame With respect to a coordinate frame whose origin coincides with the body's center of mass for τ(torque) and an inertial frame of reference for F(force), they can be expressed in matrix form as: : \left(\begin \\ \end\right) = \left(\begin m & 0 \\ 0 & _ \end\right) \left(\begin \mathbf a_ \\ \end\right) + \left(\begin 0 \\ \times _ \, \end\right), where :F = total force acting on the center of mass :''m'' = mass of the body :I3 = the 3×3 identity matrix :acm = accele ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lagrangian System
In mathematics, a Lagrangian system is a pair , consisting of a smooth fiber bundle and a Lagrangian density , which yields the Euler–Lagrange differential operator acting on sections of . In classical mechanics, many dynamical systems are Lagrangian systems. The configuration space of such a Lagrangian system is a fiber bundle over the time axis . In particular, if a reference frame is fixed. In classical field theory, all field systems are the Lagrangian ones. Lagrangians and Euler–Lagrange operators A Lagrangian density (or, simply, a Lagrangian) of order is defined as an -form, , on the -order jet manifold of . A Lagrangian can be introduced as an element of the variational bicomplex of the differential graded algebra of exterior forms on jet manifolds of . The coboundary operator of this bicomplex contains the variational operator which, acting on , defines the associated Euler–Lagrange operator . In coordinates Given bundle coordinates on a fiber bu ... [...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] |
Nonlinear Complementarity Problem
In applied mathematics Applied mathematics is the application of mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, and industry. Thus, applied mathematics is a combination of mathemati ..., a nonlinear complementarity problem (NCP) with respect to a mapping ''ƒ'' : R''n'' → R''n'', denoted by NCP''ƒ'', is to find a vector ''x'' ∈ R''n'' such that : x \geq 0,\ f(x) \geq 0 \text x^f(x)=0 where ''ƒ''(''x'') is a smooth mapping. The case of a discontinuous mapping was discussed by Habetler and Kostreva (1978). References * * Applied mathematics {{applied-math-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
