An analytical formula for an elastic thin rod shape under composite loading

The Euler problem on the stability of a thin elastic rod under compressing forces is widely known. In a number of papers this problem is generalized to finding the shape of such a rod under the simultaneous action of a compressing force and a torsional moment. The shape is determined by solving a complex nonlinear boundary value problem by numerical methods. In this paper, an approach providing a full analytical solution of the problem for a broad range of external conditions is discussed.