INDEX OF DIFFERENTIAL-ALGEBRAIC EQUATIONS GOVERNING THE DYNAMICS OF CONSTRAINED MECHANICAL SYSTEMS

A class of differential-algebraic equations (DAEs) which govern the dynamics of constrained mechanical systems is studied. Systems with material constraints and controlled systems subject to program constraints are considered. It is concluded that the index of DAEs governing the dynamics of systems with material constraints (ideal and/or nonideal) never exceeds three, whereas the index of DAEs modelling control problems of systems subject to program constraints may surpass this number. A methodology based on reducing the index value is proposed for solving DAE systems, and some observations on how to evaluate the index value dealing with the DAE system in its initial form are reported. Examples of index three and four DAE systems are included to illustrate the theoretical considerations.