caa a22 4500 606233415 CHVBK 20210128101232.0 cr unu---uuuuu 210128e20150401xx s 000 0 eng 10.1007/s10883-014-9255-2 doi (NATIONALLICENCE)springer-10.1007/s10883-014-9255-2 Rupniewski Marek Faculty of Electronics and Information Technology, Institute of Electronic Systems, Warsaw University of Technology, Nowowiejska 15/19, 00-665, Warsaw, Poland aut Singular Velocities of Even-Rank Affine Distributions [Elektronische Daten] [Marek Rupniewski] Singular curves, which are projections of singular extremals, play a special role in control theory and the theory of distributions. In this paper, we show that singular velocities, tangent to singular curves, determine affine distributions that are simultaneously of an even-rank and co-rank 2. If D is such a distribution, then its singular velocities span a distribution C D (of a rank two times smaller than that of D) that, together with its Lie square, forms the initial distribution, i.e., D = C D + C D , C D $D={C^{D}}+\left [{C^{D}},{C^{D}}\right ]$ . We also provide canonical constructions of vector fields that are C D generators, canonical differential forms that are D cogenerators, and some functional invariants related to distribution of the considered type. The Author(s), 2014 Affine distributions nationallicence Singular extremals nationallicence Singular curves nationallicence Journal of Dynamical and Control Systems Springer US; http://www.springer-ny.com 21/2(2015-04-01), 193-210 1079-2724 21:2<193 2015 21 10883 https://doi.org/10.1007/s10883-014-9255-2 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10883-014-9255-2 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Rupniewski Marek Faculty of Electronics and Information Technology, Institute of Electronic Systems, Warsaw University of Technology, Nowowiejska 15/19, 00-665, Warsaw, Poland aut NATIONALLICENCE 773 0- Journal of Dynamical and Control Systems Springer US; http://www.springer-ny.com 21/2(2015-04-01), 193-210 1079-2724 21:2<193 2015 21 10883