Multibody system constrained

Lubich, C., Nowak, U., Pohle, U., Engstler, C., MEXX - Numerical Software for the Integration of Constrained Mechanical Multibody Systems, Preprint SC 92-12, Konrad-Zuse-Zentrum Berlin (1992)... 

In this section we introduce the concept of implicit Runge-Kutta methods of collocation type without aiming for completeness. The use of implicit Runge-Kutta methods is quite recent in multibody dynamics. There are higher order A-stable methods in this class for simulating highly oscillatory problems as well as methods specially designed for constrained multibody systems, see Sec. 5.4.2. 

When dealing with constrained multibody systems, the situation is different, because E is singular. Here we have... 

For an application of parameter identification in the context of railway dynamics see [Gru95]. There, the complete working path from setting up measurements to special numerical methods for parameter identification for constrained multibody systems is described, see also Sec. 7.3.1. 

The extension of the approach to constrained multibody systems and differential-algebraic equations affects the formulation of the multiple shooting method and the computation of sensitivity matrices. The former requires a more sophisticated treatment because variations of initial values and parameters may no longer be consistent with the algebraic equations. The latter can be done efficiently by exploiting the fact that the number of degrees of freedom of the system is reduced due to the presence of constraints. 

Constrained multibody systems are described by index-3 DAEs. Index reduction by differentiating the constraints transforms these into an index-1 problem, for which we just described an adequate formulation for applying shooting techniques. Unfortunately, index-1 problems suffer from the so-called drift-off effect, i.e. the index-2 (velocity) and index-3 (position) constraints will be no longer met in the presence of numerical errors. Furthermore, the residual in these constraints increases with time. In Sec. 5 we described several projection techniques to overcome this problem. After applying modifications to the index-2 and index-3 constraints to cover the situation of inconsistent iterates for the initial values Sq previous... 

Ch. Lubich, Extrapolation Integrators for Constrained Multibody Systems, IMPACT Comp. Sci. Eng., 3 (1991), 213-234. 

M. Sofer H. Brauchli, Hamiltonian Description of Holonomically Constrained Multibody Systems (submitted for publication). 

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