Ants and bracket generating distributions in dimensions 5 and 6 (Q2103668)

A mechanical system of three ants is considered on the floor. Its dynamics is determined by two rules. The first rule (Rule A) equips the 6-dimensional configuration space of the ants with a structure of a homogeneous (3, 6) distribution, while the second rule (Rule B) foliates the configuration space onto 5-dimensional submanifolds consisting of configuration points defining triangles of equal area on the plane. Each of these manifolds is equipped with a homogeneous (2, 3, 5) distribution. The symmetry properties and the local invariants of the velocity distributions of the system are determined in both cases (Rule A and Rule B). Moreover, the singular trajectories (abnormal extremals) of the corresponding distributions are studied in the case of Rule B.