Discrete Models of Codimension-Two Singularities of Goursat Flags of Arbitrary Length with One Flag's Member in Singular Position

Generic germs of Goursat distributions (special subbundles in tangent bundles having the flag of consecutive Lie squares of ranks growing always by 1) were classified a century ago by von Weber; his discrete models are the chained systems that are well known in control theory. Germs of codimension 1, for Goursat distributions of all coranks, were classified by us in 1999. These singularities are simple as well. Singularities of codimension 2 of Goursat flags of arbitrary corank split into two geometrically distinct classes. In this paper we show that one of these classes consists of simple germs, and give a list of discrete models for them. This is in contrast with the fact that in the second class there do exist singularities of modality at least two.