...Peter Betsch; Ralf Siebert; Nicolas Sänger The formulation of multibody dynamics in terms of natural coordinates (NCs) leads to equations of motion in the form of differential-algebraic equations (DAEs). A characteristic feature of the natural coordinates approach is a constant mass matrix...

... understanding of the causes of accidents and derailments. longitudinal train forces coupler geometric nonlinearities noninertial coordinates railroad vehicle dynamics multibody systems couplings differential algebraic equations kinematics Newton-Raphson method railways vehicle dynamics...

...Shih-Tin Lin; Ming-Wen Chen The dynamic equations of motion of the constrained multibody mechanical system are mixed differential-algebraic equations (DAEs). The numerical solution of the DAE systems solved using ordinary-differential equation (ODE) solvers may suffer from constraint drift...

... method was developed for efficiently approximating fractional order operators and where elements of the present differential algebraic equation (DAE) formulation were introduced. The DAE system developed here for arbitrary orders of the fractional derivative includes an added block of equations for each...

... of the control constraint. An alternative condition is formulated, based on the practical observation that differential-algebraic equations need to be integrated using implicit algorithms, thus naturally leading to the solution of the problem in form of matrix pencil. The analogy with the representation...

...Sachit Rao; Vadim Utkin; Martin Buss We offer a technique, motivated by feedback control and specifically sliding mode control, for the simulation of differential-algebraic equations (DAEs) that describe common engineering systems such as constrained multibody mechanical structures and electric...

... components such as continuum bodies and geometrically exact beams and shells are discretized in space by using nonlinear finite element methods. The motion of the resulting discrete systems are governed by a uniform set of differential-algebraic equations (DAEs). This makes possible the application...

...Olivier A. Bauchau; Alexander Epple; Carlo L. Bottasso This paper addresses practical issues associated with the numerical enforcement of constraints in flexible multibody systems, which are characterized by index-3 differential algebraic equations (DAEs). The need to scale the equations of motion...

...Pierre Joli; Nicolas Séguy; Zhi-Qiang Feng In this paper, a modular modeling approach of multibody systems adapted to interactive simulation is presented. This work is based on the study of the stability of two differential algebraic equation solvers. The first one is based on the acceleration...

... index differential algebraic equations, based on index reduction techniques, are reviewed and discussed. Constraint violation stabilization techniques that have been developed to control constraint drift are also reviewed. These techniques are used in conjunction with algorithms that do not exactly...

... problems. Next, methods based on the use of Lagrange’s equation of the first kind, which are index-3 differential-algebraic equations in the presence of holonomic constraints, are reviewed. Methods leading to a minimum set of equations are discussed; in view of the numerical difficulties associated...

...-Taylor (HHT) implicit method and is tailored to answer the challenges posed by the numerical solution of index 3 differential-algebraic equations that govern the time evolution of a multibody system. One of the salient attributes of the algorithm is the good conditioning of the Jacobian matrix associated...

...Dan Negrut; Jose L. Ortiz The paper presents an approach to linearize the set of index 3 nonlinear differential algebraic equations that govern the dynamics of constrained mechanical systems. The proposed method handles heterogeneous systems that might contain flexible bodies, friction, control...