Resolution of the conic spring catastrophe

A mechanical system shows a "catastrophical" behaviour whenever the response in equilibrium problems is not a "function" on the proper configuration space. These Pathologies are usually overcome by the well-known unfolding techniques, which increase the dimensionality of the configuration space. In this, note we shall discuss an example of catastrophical behaviour in which the pathologies occur because a wrong global topology is assumed. We shall show that a different unsuspected choice of configuration space, which does not modify the dimensionality imposed by the number of physical degrees of freedom, is suited to "regularize" the situation.