M. Borri, C.L. Bottasso, L. Trainelli

An Embedded Projection Method for Index-3 Constrained Mechanical Systems

in J.A.C. Ambròsio, M. Kleiber (eds.), Computational Aspects of Nonlinear Structural Systems with Large Rigid Body Motion, NATO Science Series III: Computer and system sciences, vol. 179, IOS Press, Amsterdam (2001).

Abstract

General constrained systems, such as those modeling the dynamics of multibody systems, control systems and chemical processes, typically involve the solution of differential-algebraic equations (DAEs). The reliable solution of high-order DAEs can still be considered an unsolved problem under many respects. In this paper we present the `Embedded Projection Method' (EPM), a novel approach to the solution of index-3 constrained mechanical systems designed to eliminate most of the numerical difficulties related to the solution of DAEs, while preserving generality. The constraints are enforced at both the position and velocity levels employing differentiated multipliers, resulting in a complete uncoupling of the algebraic and differential parts of the problem. This way, the two subproblems can be solved separately. Furthermore, one obtains an ordinary differential equation (ODE) involving a new, modified state vector representing an unconstrained quantity. Any suitable ODE integration algorithm can then be used, by-passing the need for specialized DAE solvers.