Nonideal Constraints and Lagrangian Dynamics

This paper deals with mechanical systems subjected to a general class of non-ideal equality constraints. It provides the explicit equations of motion for such systems when subjected to such nonideal, holonomic and∕or nonholonomic, constraints. It bases Lagrangian dynamics on a new and more general principle, of which D'Alembert's principle then becomes a special case applicable only when the constraints become ideal. By expanding its perview, it allows Lagrangian dynamics to be directly applicable to many situations of practical importance where non-ideal constraints arise, such as when there is sliding Coulomb friction.