ABSTRACT
In Chapters 2 and 5, we present a unified dynamic model (2.199) and a unified dynamic control model (5.3) for a constrained system. Both models are derived based on the generalized programmed motion equations (GPME). The unified dynamics (2.199) can incorporate both material and non-material constraints of an arbitrary order. The two results contribute to theoretical development in both mechanics and control of constrained systems. The first contribution is an extension of the class of constraints that are merged into a dynamic model. The essential difference between our constrained dynamic model and models presented in the literature is that only material position and velocity constraints are merged into the latter models. Second, Equations (2.199) are in the reduced-state form. The third contribution relates to control, and it is the introduction of the unified formulation of constraints (3.78). Also, (5.3) is competitive to dynamic control models control theory uses, because it is free of the constraint reaction forces.
