Modified Extended Lie-Group Method for Hessenberg Differential Algebraic Equations with Index-3

Hessenberg differential algebraic equations (Hessenberg-DAEs) with a high index play critical role in the modeling of mechanical systems and multibody dynamics. Motivated by widely used Lie-group equation (LGDAE) method, which handles index-2 systems, we first propose modified extended (MELGDAE) method for solving index-3 Hessenberg-DAEs then provide theoretical analysis to deepen foundation MELGDAE method. Moreover, performance is compared standard methods RADAU MEBDF on -3 DAE it demonstrated that integrator exhibits competitive terms accuracy preservation constraints. In particular, all variables achieve second-order convergence using suggests potential extension an 4 or higher.