Application of the GSSSS family of algorithms to the natural index 3 differential-algebraic equations of multibody dynamics.

Abstract

Growing interest in the simulation of constrained multibody systems has prompted the development of a variety of time integration methods for the differential-algebraic equations (DAEs) inherent to these systems. The vast majority of these methods require reformulation of the natural index 3 equations of motion leading to additional computational cost and the need to control drift phenomena, citing instability of direct index 3 methods. This research sought within the generalized single step single solve (GSSSS) family of algorithms an algorithm and framework capable of overcoming the instability and problems encountered by previous researchers. A precise understanding of the equation of motion time level concept as well as novel methods for extending linear parent algorithms to nonlinear dynamic applications enabled a depth of search unique to the area. In the end, an algorithmic framework is identified which overcomes previous limitations and is capable of providing stable, robust, and accurate integration of index 3 DAEs for both rigid and rigid/flexible multibody dynamics applications.