ABSTRACT
Joseph L. C. Lagrange developed a general treatment of dynamical systems formulated from the scalar quantities of kinetic energy, potential energy, and work. Lagrange's equations are in terms of generalized coordinates, and preliminary to discussing these equations. Generalized coordinates are any set of independent coordinates equal in number to the degrees of freedom of the system. In more complex systems, it is often convenient to describe the system in terms of coordinates, some of which may not be independent. Such coordinates may be related to each other by constraint equations. Constraints are called holonomic if the excess coordinates can be eliminated through equations of constraint. The advantage of the virtual work method over the vector method is considerably greater for multi-degree of freedom (DOF) systems. The virtual work method overcame the limitations of both earlier methods and proved to be a powerful tool for systems of higher DOF.
