EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 21 / No 4 (October-December 2015) ESAIM: COCV, 21 4 (2015) 958-988 References
Free Access
Issue
ESAIM: COCV
Volume 21, Number 4, October-December 2015
Page(s) 958 - 988
DOI https://doi.org/10.1051/cocv/2015027
Published online 30 June 2015
  1. A.A. Agrachev, Geometry of optimal control problems and Hamiltonian systems. In: Nonlinear and Optimal Control Theory, Lect. Notes Math. CIME, 1932. Springer Verlag (2008) 1–59. [Google Scholar]
  2. A.A. Agrachev and D. Barilari, Sub-Riemannian structures on 3D Lie groups, J. Dyn. Control Syst. 18 (2012) 21–44. [Google Scholar]
  3. A.A. Agrachev and Yu.L. Sachkov, Control Theory from the Geometric Viewpoint. Vol. 87 of Encycl. Math. Sci. Springer-Verlag (2004). [Google Scholar]
  4. A.A. Agrachev, D. Barilari and U. Boscain, Introduction to Riemannian and sub-Riemannian geometry. Lect. Notes. Preprint (2014). Available at https://www.imj-prg.fr/˜davide.barilari/Notes.php. [Google Scholar]
  5. A.A. Agrachev, B. Bonnard, M. Chyba and I. Kupka, Sub-Riemannian sphere in Martinet flat case. ESAIM: COCV 2 (1997) 377–448. [CrossRef] [EDP Sciences] [Google Scholar]
  6. A.A. Ardentov and Yu.L. Sachkov, Extremal trajectories in nilpotent sub-Riemannian problem on the Engel group. Sbornik: Math. 202 (2011) 1593–1615. [CrossRef] [Google Scholar]
  7. A.A. Ardentov and Yu.L. Sachkov, Conjugate points in nilpotent sub-Riemannian problem on the Engel group. J. Math. Sci. 195 (2013) 369–390. [CrossRef] [MathSciNet] [Google Scholar]
  8. D.M. Almeida, Sub-Riemannian homogeneous spaces of Engel type. J. Dyn. Control Syst. 20 (2014) 149–166. [CrossRef] [MathSciNet] [Google Scholar]
  9. V.N. Berestovskii and I.A. Zubareva, Shapes of spheres of special nonholonomic left-invariant intrinsic metrics on some Lie groups, Siber. Math. J. 42 (2001) 613–628. [CrossRef] [Google Scholar]
  10. B. Bonnard and M. Chyba, Singular Trajectories and their Role in Control Theory. Springer (2003). [Google Scholar]
  11. U. Boscain and F. Rossi, Invariant Carnot-Caratheodory metrics on S 3 , SO (3), SL (2) and Lens spaces. SIAM J. Control Optim. 47 (2008) 1851–1878. [CrossRef] [MathSciNet] [Google Scholar]
  12. Y.A. Butt, Yu.L. Sachkov and A.I. Bhatti, Parametrization of extremal trajectories in sub-Riemannian problem on group of motions of pseudo euclidean plane. J. Dyn. Control Syst. 20 (2014) 341–364. [CrossRef] [MathSciNet] [Google Scholar]
  13. Y.A. Butt, Yu.L. Sachkov and A.I. Bhatti, Maxwell Strata and Conjugate Points in the Sub-Riemannian Problem on the Lie Group SH(2). Preprint arXiv:1408.2043v1 (2014). [Google Scholar]
  14. M. Christ, Nonexistence of invariant analytic hypoelliptic differential operators on nilpotent groups of step greater than two. Essays on Fourier analysis in honor of Elias M. Stein, Vol. 42 of Princeton Math. Ser. (1995) 127–145. [Google Scholar]
  15. L. Euler, Methodus inveniendi lineas curvas maximi minimive proprietate gaudentes, sive Solutio problematis isoperimitrici latissimo sensu accepti. Lausanne, Geneva (1744). [Google Scholar]
  16. J.P. Gauthier and V. Zakalyukin, On the one-step bracket-generating motion planning problem. J. Dyn. Control Syst. 11 (2005) 215–235. [CrossRef] [MathSciNet] [Google Scholar]
  17. J.P. Gauthier and V. Zakalyukin, On the motion planning problem, complexity, entropy and nonholonomic interpolation. J. Dyn. Control Syst. 12 (2006) 371–404. [CrossRef] [MathSciNet] [Google Scholar]
  18. V. Jurdjevic, Geometric Control Theory. Cambridge University Press (1997). [Google Scholar]
  19. S.G. Krantz and H.R. Parks, The Implicit Function Theorem: History, Theory, and Applications. Birkauser (2001). [Google Scholar]
  20. A.E.H. Love, A Treatise on the Mathematical Theory of Elasticity. New York, Dover (1927). [Google Scholar]
  21. I. Moiseev and Yu.L. Sachkov, Maxwell strata in sub-Riemannian problem on the group of motions of a plane. ESAIM: COCV 16 (2010) 380–399. [CrossRef] [EDP Sciences] [Google Scholar]
  22. R. Montgomery, A tour of subriemannian geometries, their geodesics and applications. Vol. 94. Math. Surv. Monogr. AMS (2002). [Google Scholar]
  23. L.S. Pontryagin, V.G. Boltayanskii, R.V. Gamkrelidze and E.F. Mishchenko, The mathematical theory of optimal processes. John Wiley, New York, London (1962). [Google Scholar]
  24. Yu.L. Sachkov, Exponential map in the generalized Dido problem. Sb. Math. 194 (2003) 1331–1359. [CrossRef] [MathSciNet] [Google Scholar]
  25. Yu.L. Sachkov, Discrete symmetries in the generalized Dido problem. Sb. Math. 197 (2006) 235–257. [CrossRef] [MathSciNet] [Google Scholar]
  26. Yu.L. Sachkov, The Maxwell set in the generalized Dido problem. Sb. Math. 197 (2006) 595–621. [CrossRef] [MathSciNet] [Google Scholar]
  27. Yu.L. Sachkov, Complete description of the Maxwell strata in the generalized Dido problem. Sb. Math. 197 (2006) 901–950. [CrossRef] [MathSciNet] [Google Scholar]
  28. Yu.L. Sachkov, Maxwell strata in Euler’s elastic problem. J. Dyn. Control Syst. 14 (2008) 169–234. [CrossRef] [MathSciNet] [Google Scholar]
  29. Yu.L. Sachkov, Conjugate points in Euler’s elastic problem. J. Dyn. Control Syst. Springer, New York (2008) 14 409–439. [Google Scholar]
  30. Yu.L. Sachkov, Conjugate and cut time in sub-Riemannian problem on the group of motions of a plane. ESAIM: COCV 16 (2010) 1018–1039. [CrossRef] [EDP Sciences] [Google Scholar]
  31. Yu.L. Sachkov, Cut locus and optimal synthesis in the sub-Riemannian problem on the group of motions of a plane. ESAIM: COCV 17 (2011) 293–321. [CrossRef] [EDP Sciences] [Google Scholar]
  32. Yu. L. Sachkov and E.F. Sachkova, Exponential mapping in Euler’s elastic problem. J. Dyn. Control Syst. 20 (2014) 443–464. [CrossRef] [MathSciNet] [Google Scholar]
  33. F. Trèves, Analytic hypo-ellipticity of a class of pseudodifferential operators with double characteristics and applications to the Formula -Neumann problem. Commun. Partial Differ. Equ. 3 (1978) 475–642. [CrossRef] [Google Scholar]
  34. A.M. Vershik and V.Ya. Gershkovich, Nonholonomic dynamical systems, geometry of distributions and variational problems. Dynamical Systems VII. Encycl. Math. Sci. (1990) 4–79. [Google Scholar]
  35. E.T. Whittaker and G.N. Watson, A Course of Modern Analysis. Cambridge University Press (1927). [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.