The Principle of Removing Constraints

Mathematically speaking an equilibrium problem for a mechanical system with perfect (that Is without friction) bilateral and unilateral constraints in a conservative force field is equivalent to general mathematical programming problems. On the other hand, every maximalization problem with constraints can be interpreted as an equilibrium problem of a mechanical system In a conservative force field defined by the function to be maximized with the constraints expressed in terms of unilateral and bilateral constraints Imposed on the system. If one uses this approach it is natural to base the theory and the solution methods on the fundamental principles of mechanics. As far as extremum problems are concerned these principles are the principle of virtual displacements (virtual work) and the principle of removing constraints (that is the principle of Lagrange multipliers); that is the fundamentals of Lagrange1s analytical mechanics.