| This dissertation develops in a unified manner a new and simple approach for the modeling and controlling of general nonlinear constrained mechanical systems. Since, in general, the description of constrained mechanical systems is highly nonlinear, the determination of the equations of motion of such highly nonlinear constrained mechanical systems is considered one of the central problems in analytical dynamics. Even though this problem has been the focus of numerous studies, several questions remain unanswered at the present time. Of particular importance among these questions is an appropriate approach to obtaining the equations of motion for constrained mechanical systems when the mass matrix of the unconstrained mechanical system is singular, or if there are uncertainties in the description of the systems, what should be done to cancel the effects of this uncertainty while the constrained equations of motion are being derived. Moreover, misinterpretations persist concerning the fundamental conceptualizations for deriving these constrained equations of motion.;The theoretical framework developed in this dissertation provides a concrete explanation that deals with those fundamental conceptualizations for deriving the equations of motion for general nonlinear constrained mechanical systems. Utilizing these fundamental conceptualizations, an explicit constrained equation of motion that works with systems containing either positive semi-definite or positive definite mass matrices is also further developed. And when considering uncertainties, the explicit equation of motion for nonlinear constrained mechanical systems has been modified by augmenting additional additive controllers that are able to guarantee tracking of reference trajectories of the system with no uncertainty assumed. The new, simple, general, and closed-form equations of motion for nonlinear constrained uncertain mechanical systems are thus developed. The results herein provide deeper insights into the behavior of constrained motion and open up new approaches to modeling complex, uncertain, constrained mechanical systems, such as those encountered in real-life multi-body dynamics. |
