Free access
Issue
ESAIM: COCV
Volume 16, Number 2, April-June 2010
Page(s) 380 - 399
DOI http://dx.doi.org/10.1051/cocv/2009004
Published online 21 April 2009
  1. A.A. Agrachev, Exponential mappings for contact sub-Riemannian structures. J. Dyn. Control Systems 2 (1996) 321–358. [CrossRef]
  2. A.A. Agrachev and Yu.L. Sachkov, Control Theory from the Geometric Viewpoint. Springer-Verlag, Berlin (2004).
  3. A.M. Bloch, J. Baillieul, P.E. Crouch and J. Marsden, Nonholonomic Mechanics and Control. Springer (2003).
  4. U. Boscain and F. Rossi, Invariant Carnot-Caratheodory metrics on S3, SO(3), SL(2) and Lens Spaces. SIAM J. Control Optim. 47 (2008) 1851–1878. [CrossRef] [MathSciNet]
  5. R. Brockett, Control theory and singular Riemannian geometry, in New Directions in Applied Mathematics, P. Hilton and G. Young Eds., Springer-Verlag, New York (1981) 11–27.
  6. C. El-Alaoui, J.P. Gauthier and I. Kupka, Small sub-Riemannian balls on Formula . J. Dyn. Control Systems 2 (1996) 359–421. [CrossRef]
  7. V. Jurdjevic, Geometric Control Theory. Cambridge University Press (1997).
  8. J.P. Laumond, Nonholonomic motion planning for mobile robots, Lecture notes in Control and Information Sciences 229. Springer (1998).
  9. F. Monroy-Perez and A. Anzaldo-Meneses, The step-2 nilpotent (n, n(n+1)/2) sub-Riemannian geometry. J. Dyn. Control Systems 12 (2006) 185–216. [CrossRef]
  10. R. Montgomery, A Tour of Subriemannian Geometries, Their Geodesics and Applications. American Mathematical Society (2002).
  11. O. Myasnichenko, Nilpotent (3, 6) sub-Riemannian problem. J. Dyn. Control Systems 8 (2002) 573–597. [CrossRef]
  12. O. Myasnichenko, Nilpotent (n, n(n+1)/2) sub-Riemannian problem. J. Dyn. Control Systems 12 (2006) 87–95. [CrossRef]
  13. J. Petitot, The neurogeometry of pinwheels as a sub-Riemannian contact stucture. J. Physiology - Paris 97 (2003) 265–309. [CrossRef] [PubMed]
  14. L.S. Pontryagin, V.G. Boltyanskii, R.V. Gamkrelidze and E.F. Mishchenko, The mathematical theory of optimal processes. Wiley Interscience (1962).
  15. Yu.L. Sachkov, Exponential map in the generalized Dido's problem. Mat. Sbornik 194 (2003) 63–90 (in Russian). English translation in: Sb. Math. 194 (2003) 1331–1359. [CrossRef] [MathSciNet]
  16. Yu.L. Sachkov, Discrete symmetries in the generalized Dido problem. Mat. Sbornik 197 (2006) 95–116 (in Russian). English translation in: Sb. Math. 197 (2006) 235–257. [CrossRef] [MathSciNet]
  17. Yu.L. Sachkov, The Maxwell set in the generalized Dido problem. Mat. Sbornik 197 (2006) 123–150 (in Russian). English translation in: Sb. Math. 197 (2006) 595–621.
  18. Yu.L. Sachkov, Complete description of the Maxwell strata in the generalized Dido problem. Mat. Sbornik 197 (2006) 111–160 (in Russian). English translation in: Sb. Math. 197 (2006) 901–950.
  19. Yu.L. Sachkov, Maxwell strata in Euler's elastic problem. J. Dyn. Control Systems 14 (2008) 169–234. [CrossRef] [MathSciNet]
  20. Yu.L. Sachkov, Conjugate points in Euler's elastic problem. J. Dyn. Control Systems 14 (2008) 409–439. [CrossRef] [MathSciNet]
  21. Yu.L. Sachkov, Conjugate and cut time in the sub-Riemannian problem on the group of motions of a plane. ESAIM: COCV (Submitted).
  22. A.M. Vershik and V.Y. Gershkovich, Nonholonomic Dynamical Systems, Geometry of distributions and variational problems (Russian), in Itogi Nauki i Tekhniki: Sovremennye Problemy Matematiki, Fundamental'nyje Napravleniya 16, VINITI, Moscow (1987) 5–85. English translation in: Encyclopedia of Mathematical Sciences 16, Dynamical Systems 7, Springer Verlag.
  23. E.T. Whittaker and G.N. Watson, A Course of Modern Analysis, An introduction to the general theory of infinite processes and of analytic functions; with an account of principal transcendental functions. Cambridge University Press, Cambridge (1996).