Some simple mechanical systems with a post-buckling path bifurcating at infinity
It is shown, that simple structures composed of rigid bodies exist, which possess an equilibrium position, that is stable for all finite loadings, and a post-buckling path bifurcating off for the loading at infinity. This property only occurs for the perfect system as imperfect systems have a finite critical loading. Methods of singularity theory are applied to investigate this type of bifurcation. In simple cases it is possible to give the full (versal) unfolding by means of catastrophe theory. But for higher dimensional cases especially adapted concepts are considered to be the proper mean, particularly as common reduction principles do not work for this type of bifurcation. To show that bifurcation at infinity does not only occur for static problems a reference to an example from hydrodynamics is given.
simple structures composed of rigid bodies
post-buckling path bifurcating off for the loading at infinity
scientific article; zbMATH DE number 3930470