2. Definitions of nonlinear modes

The first definition was given by Rosenberg in the 1960s, but it was in the early 1990s that the theoretically most solid definition of non-linear modes was given using the theory of dynamical systems. Thus a non-linear mode is defined as « an invariant variety of dimension 2 of the phase space, tangent to a stable equilibrium point of the linearized system » (cf. [Bib2]).

For conservative systems, a non-linear mode can be defined as a « family of periodic solutions ». This definition is much more attractive because it gives access to powerful digital tools such as continuation methods. This is why this definition was chosen here, so MODE_NON_LINE allows the calculation of families of periodic solutions.