Author : A. Awane
Publisher : Springer Science & Business Media
ISBN 13 : 9401595267
Total Pages : 247 pages
Book Rating : 4.4/5 (15 download)
Book Synopsis Pfaffian Systems, k-Symplectic Systems by : A. Awane
Download or read book Pfaffian Systems, k-Symplectic Systems written by A. Awane and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of foliations and contact forms have experienced such great de velopment recently that it is natural they have implications in the field of mechanics. They form part of the framework of what Jean Dieudonne calls "Elie Cartan's great theory ofthe Pfaffian systems", and which even nowa days is still far from being exhausted. The major reference work is. without any doubt that of Elie Cartan on Pfaffian systems with five variables. In it one discovers there the bases of an algebraic classification of these systems, their methods of reduction, and the highlighting ofthe first fundamental in variants. This work opens to us, even today, a colossal field of investigation and the mystery of a ternary form containing the differential invariants of the systems with five variables always deligthts anyone who wishes to find out about them. One of the goals of this memorandum is to present this work of Cartan - which was treated even more analytically by Goursat in its lectures on Pfaffian systems - in order to expound the classifications currently known. The theory offoliations and contact forms appear in the study ofcompletely integrable Pfaffian systems of rank one. In each of these situations there is a local model described either by Frobenius' theorem, or by Darboux' theorem. It is this type of theorem which it would be desirable to have for a non-integrable Pfaffian system which may also be of rank greater than one.