Abstract
A stability analysis is presented for the analytic solution of the adjoint equations corresponding to semiexplicit index-3 differential-algebraic equations (DAE) that have a more general form than Hessenberg, particularly index-3 DAE that arise in the study of multibody system dynamics. Necessary and sufficient conditions are derived for stability of the backward analytic integration of the adjoint index-3 DAE that corresponds to a multibody system equation of motion index-3 DAE. In addition, the procedure for constructing an underlying ordinary differential equation (ODE) through the coordinate partitioning method is compared with that for constructing an essential underlying ODE, and stability is proved for the coordinate partitioning underlying ODE of the adjoint index-3 DAE.
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