Bifurcation and postbifurcation of rods

In studying elastic bifurcations the general way is to start with a variational setting. After then, the uniqueness of linear part is to be considered to find the bifurcation points and the curvature shows whether the equilibrium curve is sub- or supercritical. These methods offer no possibility to investigate even a small neighbourhood of the bifurcation point being important for possible secondary bifurcations. If we need this information, we should approach the problem in the other way. The equilibrium equation should be studied in a local form and some kind of reduction process should be realised to end up with an algebraic equation called the bifurcation equation. This equation describes the nonlinear behavior of the system in the vicinity of the bifurcation point giving information on the secondary bifurcations. Moreover it enables us to find also the effects of imperfections. In the paper the connections and advantages of both methods are discussed. As an example the buckling process in a rod is presented.