If we take the usual mechanical oscillatory system, then the expressions for the kinetic and potential energy usually have a complete quadratic form for the potential energy and an incomplete quadratic form for the expression determining the kinetic energy of the system. Choosing the appropriate coordinate systems, it is possible to carry out an inversion and obtain the complete quadratic form for expressing the kinetic energy, and incomplete form for the potential energy. The solution of the problem of simultaneous reduction of expressions to incomplete form means a transition to the main coordinates, which is possible only for some special cases. Expressions for the kinetic and potential energies simultaneously in a complete quadratic form are possible, however, this requires the introduction of additional constraints, as shown, for example, in Eliseev et al. (2006). Essentially, the possibility of reducing the expressions for kinetic and potential energies to full quadratic forms predetermines the fundamental possibilities of the “legitimacy” of introducing additional feedbacks and expanding the typical element base of the vibration protection systems.