Differential Equations

, Volume 53, Issue 3, pp 352–365 | Cite as

Degenerate abnormal trajectories in a sub-Riemannian problem with growth vector (2, 3, 5, 8)

  • Yu. L. SachkovEmail author
  • E. F. Sachkova
Control Theory


We consider the nilpotent sub-Riemannian problem with growth vector (2, 3, 5, 8). We describe and study abnormal extremals orthogonal to the cube of the distribution. We analyze the geometric properties of a two-dimensional surface in the state space on which the corresponding abnormal trajectories define optimal synthesis.


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© Pleiades Publishing, Ltd. 2017

Authors and Affiliations

  1. 1.Steklov Mathematical Institute of the Russian Academy of SciencesMoscowRussia
  2. 2.Ailamazyan Program Systems Institute of Russian Academy of SciencesYaroslavskaya oblast, Pereslavskii raion, s. Ves’kovoRussia
  3. 3.Peoples Friendship University of RussiaMoscowRussia

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