Rank-2 distributions satisfying the Goursat condition : all their local models in dimension 7 and 8
ESAIM: Control, Optimisation and Calculus of Variations (1999)
- Volume: 4, page 137-158
- ISSN: 1292-8119
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topCheaito, 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
top- [1] R. Bryant, S. Chern, R. Gardner, H. Goldschmidt and P. Griffiths, Exterior Differential Systems, MSRI Publications 18, Springer-Verlag, New York ( 1991). Zbl0726.58002MR1083148
- [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] 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] 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] 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] 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] 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] 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] 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] P. Mormul, Local models of 2-distributions in 5 dimensions everywhere fulfilling the Goursat condition (preprint Rouen), 1994).
- [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] 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] 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] 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] M. Zhitomirskii, Rigid and abnormal line subdistributions of 2-distributions. J. Dyn. Control Systems 1 ( 1995) 253-294. Zbl0970.53020MR1333773
Citations in EuDML Documents
top- Piotr Mormul, Contact hamiltonians distinguishing locally certain Goursat systems
- Piotr Mormul, Geometric classes of Goursat flags and the arithmetics of their encoding by small growth vectors
- Richard Montgomery, Michail Zhitomirskii, Geometric approach to Goursat flags
- Shun-Jie Li, Witold Respondek, Flat outputs of two-input driftless control systems
- Shun-Jie Li, Witold Respondek, Flat outputs of two-input driftless control systems
- Shun-Jie Li, Witold Respondek, Flat outputs of two-input driftless control systems
- William Pasillas-Lépine, Witold Respondek, On the Geometry of Goursat Structures
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