Abstract: A unchanged force is demonstrated as a potential force with its potential energy to solve problems in theoretical mechanics. In equilibrium problems, the potential energy can be used to establish the equilibrium conditions for a potential system subjected to unchanged forces and the stability is determined via the stationary value of the potential energy. The potential energy generalizes the conservative Lagrangian equation to a potential system with unchanged forces. For Lagrangian functions independt of the time or the generalized coordinates, the generalized energy conservation and generalized momentum conservation are obtained.

Key words:  potential energy, unchanged force, equilibrium, stability, conserved quantity