| This study presents the new, general forms of the explicit equations of motion for general mechanical systems subjected to holonomic and/or nonholonomic constraints. These constraints may or may not satisfy D'Alembert's principle.; In this dissertation we first show that the general, explicit equations of motion for mechanical systems under nonideal constraints can be obtained without any use of generalized inverses. These equations are then shown to be equivalent to those obtained using generalized inverses.; Next we derive the more general, explicit equations of motion capable of handling mechanical systems with symmetric, semi-positive definite mass matrices. These new equations are shown to be identical to ones obtained by Udwadia and Kalaba when the mass matrices become symmetric, positive definite. Examples are then provided to show that systems with singular mass matrices can really occur and to demonstrate the use of the new equations.; Subsequently, we make use of quasi-velocities as independent variables to describe constrained motion. Based on these quasi-velocities, we generalize the Poincare equations for unconstrained systems and then derive the general, explicit Poincare equations of motion for constrained mechanical systems. These new explicit Poincare equations of motion for constrained systems might be probably considered the most general, explicit equations so far obtained. |
