A purely frequency based Floquet-Hill formulation for the efficient stability computation of periodic solutions of ordinary differential systems

•The Hill's method of stability analysis is proved to be a by-product of the Harmonic Balance Method.•A nonlinear quadratic recast of the dynamical system is used for an automatic generation of the Hill's matrix.•The issue of eigenvalue sorting is solved by a robust criterion on the eigenvectors.•The method is validated by the stability computation of several canonical systems.•The complex topology of the backbone curves of a hinged-hinged beam is presented in details.