A New Numerical Technique for Index-3 DAEs Arising from Constrained Multibody Mechanical Systems

Index-3 differential-algebraic equations (DAEs) are mathematical models for the dynamics of constrained multibody mechanical systems that arise in many applications. These DAEs are known to pose a challenge to numerical methods. The purpose of this paper is to propose a new approach to efficiently solve these equations. This approach relies on an effective combination of the power series method (PSM) with the Adomian polynomials. Here, the PSM is directly applied to these DAEs without using the usual index reduction techniques, which are costly and often lead to nonphysical solutions. We expand the nonlinear terms in a series form using the Adomian polynomials to overcome the limitation of the PSM in collecting the coefficients of the power series solution. This technique has led to a simple and efficient algorithm. The domain of convergence of the power series solution is expanded by developing a multistage PSM (MSPSM). To demonstrate the efficiency of the MSPSM and show its applicability, an index-3 nonlinear DAE problem describing a two-link planar robot arm is solved. The numerical results show that the MSPSM is a powerful tool for solving the index-3 DAEs arising from constrained multibody mechanical systems.