LAGRANGIAN SYSTEMS WITH CONSTRAINTS - A GEOMETRIC APPROACH TO THE METHOD OF LAGRANGE MULTIPLIERS

A geometric approach to the method of Lagrange multipliers is presented using the framework of the tangent bundle geometry. The non-holonomic systems with constraint functions linear in the velocities are studied in the first place and then, and using this study of the non-holonomic mechanical systems as a previous result, the holonomic systems are considered. The Lagrangian inverse problem is also analysed and, finally, the theory is illustrated with several examples.