On the branching of equilibrium paths

Abstract

The local quasi-static behaviour near a compound branching point of a conservative system is analysed. General equations governing the possible regular equilibrium paths through a point where one path is known are derived, in the form of a perturbation sequence appropriate to the data. Among the consequences is an account of the analytical distinctions between smooth and abrupt bifurcations. The theory is immediately applicable to any system (or structure) whose potential energy adequately depends on a finite number of variables.