M. Borri, L. Trainelli, A. Croce

An Index Reduction Method in Holonomic Systems Dynamics

presented at the Second M.I.T. Conference on Computational Fluid and Solid Mechanics, Massachusetts Institute of Technology, Cambridge, MA, USA, June 17-20, 2003.

Abstract

We present the application of the Embedded Projection Method, a general methodology to reduce the DAE index to 1, to holonomically constrained mechanical systems, which are naturally formulated in terms of index-3 DAE problems. This procedure represents an extension to higher index of that already presented in Ref. [3] for non-holonomic systems. The holonomic case is more complex, requiring the introduction of modified coordinates in addition to modified momenta and differentiated multipliers. Eventually we recover the same qualitative result as in the non-holonomic case: a complete uncoupling of the algebraic and differential parts of the problem which implies a gentler numerical behavior with enhanced accuracy and stability. As a consequence, the numerical integration of a index-higher-than-2 DAE can be performed by any suitable ODE integrator, by-passing the need for a specialized DAE solver.