A Hamilton principle based direct variational method for asymptotic determination of the stability / instability boundaries of Mathieu’s equation is presented. A generalization of the conventional Hamilton principle connected with the presence of time-dependent parameters in the system of the Lagrangian is proposed. These variable system parameters are treated as additional generalized coordinates and subjected to similar variations. The resulting energetic expressions are interpreted as an energy stability criterion. Its relation with existing non-conservative system energy tests is also discussed.