Abstract
The dynamical simulation of mechanical multibody systems has stimulated the development of theory and numerical methods for higher index differential-algebraic equations (DAEs) for more than three decades. The equations of motion are linearly implicit second order differential equations. For constrained systems, they form an index-3 DAE with a specific structure that is exploited in theoretical investigations as well as in the numerical solution. In the present survey paper, we give an introduction to this field of research with focus on classical and more recent solution techniques for the time integration of constrained mechanical systems in multibody system dynamics. Part of the material is devoted to topics of current research like multibody system models with nonlinear configuration spaces or systems with redundant constraints.
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