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Multibody Dynamics and Differential Algebraic Equations

Patrick Wijckmans

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Project description	Multibody systems are mechanical systems which are interconnected so that large relative motion between the bodies may occur. These interconnections consist of joints, that constrain the relative motion between the interconnected bodies and are the cause of constraining forces, and force elements. A wide variety of mechanical systems, e.g. vehicles and robots, can be modeled in this way. Dynamic simulations are an important part of computer aided design (CAD). Furthermore, these simulations are very important in the crash safety field, where they can be used for the analysis of the crash response of vehicles, and for the design of safety devises such as e.g. airbags. A variety of powerful algorithms for efficiently generating the highly nonlinear equations of motion of multibody systems have been created by the developments in multibody dynamics. This made it possible to derive the governing equations for even very complex and realistic mechanical systems. In general the motion of multibody systems is described by so called differential algebraic equations (DAEs), i.e. a set of differential equations coupled with algebraic constraints. This project primarily deals with the numerical solution of these DAEs. However, standard methods fail since is appears to be very difficult to satisfy the algebraic constraints in a numerical simulation. Hence, numerical methods which minimize the drift off from the constraints are developed.
Recent reference	Wijckmans P.M.E.J, Differential Algebraic Equations, RANA Report 93-02, Eindhoven University of Technology, 1993.