Nonregular Abnormal Extremals of 2-Distribution: Existence, Second Variation, and Rigidity Academic Article uri icon


  • We study existence and rigidity (W1-isolatedness) of nonregular abnormal extremals of completely nonholonomic 2-distribution (nonregularity means that such extremals do not satisfy the strong generalized Legendre-Clebsch condition). Introducing the notion of diagonal form of the second variation, we generalize some results of A. Agrachev and A. Sarychev about rigidity of regular abnormal extremals to the nonregular case. In order to reduce the second variation to the diagonal form, we construct a special curve of Lagrangian subspaces, a Jacobi curve. We show that certain geometric properties of this curve (like simplicity) imply the rigidity of the corresponding abnormal extremal.

published proceedings

  • Journal of Dynamical and Control Systems

author list (cited authors)

  • Zelenko, I.

citation count

  • 13

complete list of authors

  • Zelenko, I

publication date

  • January 1999