Symmetries of flat rank two distributions and sub-Riemannian structures

Transactions of the American Mathematical Society

Volumn 356, Issue 2, 2004, Pages 457-494

  Sachkov, Yuri L ^a  

^a PROGRAM SYSTEMS INSTITUTE   (Russian Federation)

Author keywords

Distributions; Sub Riemannian geometry; Sub Riemannian structures; Symmetries

Indexed keywords

EID: 0742271504     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9947-03-03342-7     Document Type: Article

References (17)

1. A. A. Agrachev and Vu. L. Sachkov, An Intrinsic Approach to the Control of Rolling Bodies, Proceedings of the 38-th IEEE Conference on Decision and Control, vol. 1, Phoenix, Arizona, USA, December 7-10, 1999, 431-435.
2. A. A. Agrachev and A. A. Sarychev, Filtration of a Lie algebra of vector fields and the nilpotent approximation of controllable systems, Dokl. Akad. Nauk SSSR, 295 (1987), English transl. in Soviet Math. Dokl., 36 (1988), 104-108. MR 88j:93015
3. A. A. Agrachev and A. A. Sarychev, Filtration of a Lie algebra of vector fields and the nilpotent approximation of controllable systems, Dokl. Akad. Nauk SSSR, 295 (1987), English transl. in Soviet Math. Dokl., 36 (1988), 104-108. MR 88j:93015
4. A. Bellaiche, The tangent space in sub-Riemannian Geometry, In Sub-Riemannian Geometry, A. Bellaiche and J.-J. Risler, eds., Birkhäuser, Basel, Swizerland, 1996.
5. A. V. Bocharov, A. M. Verbovetsky, A. M. Vinogradov et al., Symmetries and conservation laws for differential equations of mathematical physics (in Russian), Moscow, 1997. English translation in Translations of Mathematical Monographs 182, American Mathematical Society, Providence, RI, 1999. MR 2000f:58076
6. A. V. Bocharov, A. M. Verbovetsky, A. M. Vinogradov et al., Symmetries and conservation laws for differential equations of mathematical physics (in Russian), Moscow, 1997. English translation in Translations of Mathematical Monographs 182, American Mathematical Society, Providence, RI, 1999. MR 2000f:58076
7. R. L. Bryant, S. S. Chern, R. B. Gardner, H. L. Goldshmidt, and P. A. Griffits, Exterior differential systems, Springer-Verlag, 1984.
8. E. Cartan, Les systèmes de Pfaff a cinque variables et les équations aux derivées partielles du second ordre, Ann. Sci. École Normale 27 (1910), 3: 109-192.
9. V. Ya. Gershkovich, Engel structures on four dimensional manifolds, Preprint series No. 10, The University of Melbourne, Dept. of Mathematics, 1992.
10. V. Jurdjevic, Geometric control theory, Cambridge Studies in Advanced Mathematics 52, Cambridge University Press, 1997. MR 98a:93002
11. J. P. Laumond, Nonholonomic motion planning for mobile robots, LAAS Report 98211, May 1998, LAAS-CNRS, Toulouse, France.
12. A. Marigo and A. Bicchi, Rolling bodies with regular surface: the holonomic case, In Differential geometry and control: Summer Research Institute on Differential Geometry and Control, June 29-July 19, 1997, Univ. Colorado, Boulder, G. Ferreyra et al., eds., Proc. Sympos. Pure Math. 64, Amer. Math. Soc., Providence, RI, 1999, 241-256. MR 99g:70016
13. M. M. Postnikov, Lie groups and Lie algebras (in Russian), Nauka, Moscow, 1982. MR 85b:22001
14. M. Vendittelli, J. P. Laumond, and G. Oriolo, Steering nonholonomic systems via nilpotent approximations: The general two-trailer system, IEEE International Conference on Robotics and Automation, May 10-15, Detroit, MI, 1999.
15. A. M. Vershik and V. Ya. Gershkovich, Nonholonomic dynamical systems. Geometry of distributions and variational problems. (Russian) In Itogi Nauki i Tekhniki: Sovremennye Problemy Matematiki, Fundamentalnye Napravieniya, Vol. 16, VINITI, Moscow, 1987, 5-85. English translation in Encyclopedia of Math. Sci., Vol. 16; Dynamical Systems VII, Springer-Verlag, 1991.
16. A. M. Vershik and V. Ya. Gershkovich, Nonholonomic dynamical systems. Geometry of distributions and variational problems. (Russian) In Itogi Nauki i Tekhniki: Sovremennye Problemy Matematiki, Fundamentalnye Napravieniya, Vol. 16, VINITI, Moscow, 1987, 5-85. English translation in Encyclopedia of Math. Sci., Vol. 16; Dynamical Systems VII, Springer-Verlag, 1991.
17. D.P. Zhelobenko and A.I. Shtern, Representations of Lie groups (in Russian), Nauka, Moscow, 1983. MR 85g:22001