Approximate Analytical Solution of Index-2 DAEs Arising from Constrained Multibody Systems

Abstract

Constrained multibody mechanical systems are used in various applications. These systems often lead to index-2 or index-3 differential-algebraic equations (DAEs), which are known to pose a challenge to numerical integration methods. This paper develops a novel approach to solve index- 2 DAEs which describe the dynamics of constrained multibody mechanical systems. The method, called PSMAP, relies on effective combination of the power series method (PSM) with Adomian polynomials (AP). To overcome the limitation of the PSM, the PSMAP expands nonlinear terms once in series form using AP. Further, by exploiting an important property of AP, a nonsingular linear algebraic system for the coefficients of the power series solution is derived and solved. To extend the domain of the power series solution, a multistage PSMAP is developed. The main advantage of our technique is that it applies directly to the DAE without the need for complex or costly transformations like index-reductions. Consequently, the PSMAP considerably reduces the computation work, leads to simple algorithm and avoids constraints violation. To demonstrate the efficiency of the PSMAP, two examples of two-link planar robotic systems are solved. Numerical results show that the PSMAP is a powerful tool to solve this class of DAEs.