On the conditional total stability of equilibrium for mechanical systems

In connection with the problem of observability, properties of total stability restricted to classes of perturbations of the governing equations are discussed for the equilibrium of holonomic mechanical systems. These systems are subject to positional conservative and dissipative forces. The particular case of a null dissipation is included. The perturbations to which the total stability is restricted are those obtained by modifying the kinetic energy, the potential of the conservative force, and the dissipative terms, without altering the Lagrangian form of the equations of the motion.