Regarding constrained mechanical systems, we are faced with index-3 differential-algebraic equation (DAE) systems. Direct discretization of the index-3 DAE systems only enforces the position constraints to be fulfilled at the integration-time points, but not the hidden constraints. In addition, order reduction effects are observed in the velocity variables and the Lagrange multipliers. In literature, different numerical techniques have been suggested to reduce the index of the system and to handle the numerical integration of constrained mechanical systems. This paper deals with an alternative concept, called collocated constraints approach. We present index-2 and index-1 formulations in combination with implicit Runge–Kutta methods. Compared with the direct discretization of the index-3 DAE system, the proposed method enforces also the constraints on velocity and—in case of the index-1 formulation—the constraints on acceleration level. The proposed method may very easily be implemented in standard Runge–Kutta solvers. Here, we only discuss mechanical systems. The presented approach can, however, also be applied for solving nonmechanical higher-index DAE systems.
Solving Differential-Algebraic Equation Systems: Alternative Index-2 and Index-1 Approaches for Constrained Mechanical Systems
Institute of Applied Dynamics,
Technical University Darmstadt,
Darmstadt 64287, Germany
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received November 23, 2014; final manuscript received August 6, 2015; published online November 13, 2015. Assoc. Editor: Dan Negrut.
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Schweizer, B., and Li, P. (November 13, 2015). "Solving Differential-Algebraic Equation Systems: Alternative Index-2 and Index-1 Approaches for Constrained Mechanical Systems." ASME. J. Comput. Nonlinear Dynam. July 2016; 11(4): 044501. https://doi.org/10.1115/1.4031287
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