Introduction
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Nonlinear modes are a mathematical tool that allows the interpretation of non-linear dynamic phenomena. They are an extension of the eigenmodes [:ref:`R5.01.01 <R5.01.01>`] used to interpret linear dynamic systems.

The operator MODE_NON_LINE makes it possible to calculate the non-linear modes of dynamic systems with localized shock nonlinearities.

The definition of non-linear modes will be recalled, then the non-linearities of shocks supported by the operator (unilateral, bilateral and annular contact) will be described, and finally the algorithm used will be described. The latter is a combination of the harmonic balancing method (EH) and the numerical asymptotic method (MAN), which is called EHMAN (cf. [:ref:`Bib1 <Bib1>`]).

This documentation is not an exhaustive presentation of non-linear modes. It simply recalls the main hypotheses under which we can search for non-linear modes using MODE_NON_LINE, as well as the principles adopted for the representation of nonlinearity and the basic algorithmic elements. For a more complete overview, and implementation details, refer the reader to reference [:ref:`Bib1 <Bib1>`].