Rank-2 distributions satisfying the Goursat condition : all their local models in dimension 7 and 8

Mohamad Cheaito; Piotr Mormul

ESAIM: Control, Optimisation and Calculus of Variations (1999)

  • Volume: 4, page 137-158
  • ISSN: 1292-8119

How to cite

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Cheaito, Mohamad, and Mormul, Piotr. "Rank-2 distributions satisfying the Goursat condition : all their local models in dimension 7 and 8." ESAIM: Control, Optimisation and Calculus of Variations 4 (1999): 137-158. <http://eudml.org/doc/90538>.

@article{Cheaito1999,
author = {Cheaito, Mohamad, Mormul, Piotr},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {distribution; Goursat condition; flag; derived system; small growth vector},
language = {eng},
pages = {137-158},
publisher = {EDP Sciences},
title = {Rank-2 distributions satisfying the Goursat condition : all their local models in dimension 7 and 8},
url = {http://eudml.org/doc/90538},
volume = {4},
year = {1999},
}

TY - JOUR
AU - Cheaito, Mohamad
AU - Mormul, Piotr
TI - Rank-2 distributions satisfying the Goursat condition : all their local models in dimension 7 and 8
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 1999
PB - EDP Sciences
VL - 4
SP - 137
EP - 158
LA - eng
KW - distribution; Goursat condition; flag; derived system; small growth vector
UR - http://eudml.org/doc/90538
ER -

References

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  2. [2] E. Cartan, Les systèmes de Pfaff à cinq variables et les équations aux dérivées partielles du second ordre. Ann. Ec. Norm., XXVII. 3 ( 1910) 109-192. Zbl41.0417.01MR1509120JFM41.0417.01
  3. [3] M. Gaspar, Sobre la clasificacion de sistemas de Pfaff en bandera, in: Proceedings of 10th Spanish-Portuguese Conference on Math., Univ. of Murcia ( 1985) 67-74 (in Spanish). MR844788
  4. [4] M. Gaspar, A. Kumpera and C. Ruiz, Sur les systèmes de Pfaff en drapeau. An. Acad. Brasil. Cienc. 55 ( 1983) 225-229. Zbl0529.58002MR728810
  5. [5] A. Giaro, A. Kumpera and C. Ruiz, Sur la lecture correcte d'un résultat d'Elie Cartan. C. R. Acad. Sci. Paris 287 ( 1978) 241-244. Zbl0398.58003MR507769
  6. [6] F. Jean, The car with N trailers: characterisation of the singular configurations. ESAIM: Contr. Optim. Cal. Var. (URL: http://www.emath.fr/cocv/) 1 ( 1996) 241-266. Zbl0874.93033MR1411581
  7. [7] A. Kumpera and C. Ruiz, Sur l'équivalence locale des systèmes de Pfaff en drapeau, in: Monge-Ampère Equations and Related Topics, Inst. Alta Math., Rome ( 1982) 201-248. Zbl0516.58004MR704040
  8. [8] J.-P. Laumond, Controllability of a multibody mobile robot. in: Proc. of the International Conference on Advanced Robotics and Automation, Pisa ( 1991) 1033-1038. 
  9. [9] J.-P. Laumond and T. Simeon, Motion planning for a two degrees of freedom mobile robot with towing, LAAS/CNRS Report 89 148, Toulouse ( 1989). 
  10. [10] P. Mormul, Local models of 2-distributions in 5 dimensions everywhere fulfilling the Goursat condition (preprint Rouen), 1994). 
  11. [11] P. Mormul, Local classification of rank-2 distributions satisfying the Goursat condition in dimension 9, preprint 582, Inst. of Math., Polish Acad. Sci., Warsaw, January ( 1998). 
  12. [12] R. Murray, Nilpotent bases for a class of nonintegrable distributions with applications to trajectory generation for nonholonomic systems. Math. Control Signals Systems 7 ( 1994) 58-75. Zbl0825.93319MR1359021
  13. [13] M. Zhitomirskii, Normal forms of germs of distributions with a fixed segment of growth vector (English translation). Leningrad Math. J. 2 ( 1991) 1043-1065. Zbl0732.58004MR1086448
  14. [14] M. Zhitomirskii, Singularities and normal forms of smooth distributions, in: Geometry in Nonlinear Control and Differential Inclusions, Banach Center Publications, Vol. 32, Warsaw ( 1995) 395-409. Zbl0841.58005MR1364442
  15. [15] M. Zhitomirskii, Rigid and abnormal line subdistributions of 2-distributions. J. Dyn. Control Systems 1 ( 1995) 253-294. Zbl0970.53020MR1333773

Citations in EuDML Documents

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  1. Piotr Mormul, Contact hamiltonians distinguishing locally certain Goursat systems
  2. Piotr Mormul, Geometric classes of Goursat flags and the arithmetics of their encoding by small growth vectors
  3. Richard Montgomery, Michail Zhitomirskii, Geometric approach to Goursat flags
  4. Shun-Jie Li, Witold Respondek, Flat outputs of two-input driftless control systems
  5. Shun-Jie Li, Witold Respondek, Flat outputs of two-input driftless control systems
  6. Shun-Jie Li, Witold Respondek, Flat outputs of two-input driftless control systems
  7. William Pasillas-Lépine, Witold Respondek, On the Geometry of Goursat Structures

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