Review article

Modern mathematical packages allow a simple and convenient solution of boundary value problems for systems of ordinary differential equations provided that the problem has a unique solution. In stability problems, the latter condition is not satisfied, and the direct integration of equations is not used there when finding a solution. Direct integration of equations is possible if one changes the usual order to derive the critical force. Below, this possibility is applied to equilibrium's bifurcation problems of compressed elastic rods with variable cross-section.