EQUILIBRIUM POINTS OF MECHANICAL SYSTEMS

This paper deals with the differences between regular and singular points of equilibrium states of elastic systems. The author provides a classification of singular points based on mathematical, mechanical and geometrical approaches. Aspects concerning nondegenerate (regular) critical points in which the first differential is zero and the second differential (quadratic form) is not degenerate are disclosed. The conditions of stability and instability of isolated equilibria are discussed, as well as the influence of the primary nonzero terms of the potential energy expansion on the stability of degenerate equilibria. The conditions for bifurcation loss of stability in the context of incomplete equilibrium of elastic systems are considered. It is analyzed that a necessary condition for the appearance of bifurcation points is the presence of an energetically orthogonal complement. The influence of initial geometrical imperfections on the character of stability loss is also considered.