Rank-2 distributions satisfying the Goursat condition : all their local models in dimension 7 and 8
ESAIM: Control, Optimisation and Calculus of Variations, Tome 4 (1999), pp. 137-158. 
@article{COCV_1999__4__137_0,
     author = {Cheaito, Mohamad and Mormul, Piotr},
     title = {Rank-$2$ distributions satisfying the {Goursat} condition : all their local models in dimension $7$ and $8$},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {137--158},
     publisher = {EDP-Sciences},
     volume = {4},
     year = {1999},
     mrnumber = {1816509},
     zbl = {0957.58002},
     language = {en},
     url = {http://www.numdam.org/item/COCV_1999__4__137_0/}
}
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Cheaito, Mohamad; 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, Tome 4 (1999), pp. 137-158. http://www.numdam.org/item/COCV_1999__4__137_0/

[1] R. Bryant, S. Chern, R. Gardner, H. Goldschmidt and P. Griffiths, Exterior Differential Systems, MSRI Publications 18, Springer-Verlag, New York ( 1991). | MR | Zbl

[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. | JFM | Numdam | MR

[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). | MR

[4] M. Gaspar, A. Kumpera and C. Ruiz, Sur les systèmes de Pfaff en drapeau. An. Acad. Brasil. Cienc. 55 ( 1983) 225-229. | MR | Zbl

[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. | MR | Zbl

[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. | Numdam | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[15] M. Zhitomirskii, Rigid and abnormal line subdistributions of 2-distributions. J. Dyn. Control Systems 1 ( 1995) 253-294. | MR | Zbl