Mechanical systems under servo constraints: the Lagrange's approach

The classical Lagrangean mechanics is extended to consider servo controls. A mechanical system is subject to a set of constraints. The means to realize the constraints are a set of servo controls, instead of the environment as has been considered in the classical Lagrangean mechanics. We first propose a new Lagrange's form of d'Alembert's principle for the servo case. The servo constraint problem will be solved via the Lagrange's approach. The result is then extended to solve a more complicated servo constraint problem, in which the given force and the constraint force are coupled.