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Author: Harold H. Johnson
Publisher:
ISBN:
Category :
Languages : en
Pages : 11
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Book Description
This paper concerns an equivalence relation first defined by E. Cartan for certain systems of ordinary differential equations. He called two systems absolutely equivalent if they had isomorphic prolongations. The author extends Cartan's definition to general exterior differential systems. Two exterior differential systems are absolutely equivalent if there exists a sequence of systems beginning with one and ending with the second in which for each adjacent pair one is a partial prolongation of its neighbor. Two kinds of numerical invariants are found, depending on the characters s sub o, s sub 1, . . ., s sub p. Using Kuranishi's infinite analytic mappings, the last non-zero integer among s sub o, s sub 1 ... s sub p is an absolute invariant. Other absolute invariants are computed from the sequence of prolongations of a given system.
Author: Harold H. Johnson
Publisher:
ISBN:
Category :
Languages : en
Pages : 11
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Book Description
This paper concerns an equivalence relation first defined by E. Cartan for certain systems of ordinary differential equations. He called two systems absolutely equivalent if they had isomorphic prolongations. The author extends Cartan's definition to general exterior differential systems. Two exterior differential systems are absolutely equivalent if there exists a sequence of systems beginning with one and ending with the second in which for each adjacent pair one is a partial prolongation of its neighbor. Two kinds of numerical invariants are found, depending on the characters s sub o, s sub 1, . . ., s sub p. Using Kuranishi's infinite analytic mappings, the last non-zero integer among s sub o, s sub 1 ... s sub p is an absolute invariant. Other absolute invariants are computed from the sequence of prolongations of a given system.
Author: Kichoon Yang
Publisher: Springer Science & Business Media
ISBN: 9401580685
Category : Mathematics
Languages : en
Pages : 206
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Book Description
This monograph presents a concise yet elementary account of exterior differential system theory so that it can be quickly applied to problems. The first part of the monograph, Chapters 1-5, deals with the general theory: the Cartan-Kaehler theorem is proved, the notions of involution and prolongation are carefully laid out, quasi-linear differential systems are examined in detail, and explicit examples of the Spencer cohomology groups and the characteristic variety are given. The second part of the monograph, Chapters 6 and 7, deals with applications to problems in differential geometry: the isometric embedding theorem of Cartan-Janet and its various geometric ramifications are discussed, a proof of the Andreotti-Hill theorem on the O-R embedding problem is given, and embeddings of abstract projective structures are discussed. For researchers and graduate students who would like a good introduction to exterior differential systems. This volume will also be particularly useful to those whose work involves differential geometry and partial differential equations.
Author: Robert L. Bryant
Publisher: Springer Science & Business Media
ISBN: 1461397146
Category : Mathematics
Languages : en
Pages : 483
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Book Description
This book gives a treatment of exterior differential systems. It will in clude both the general theory and various applications. An exterior differential system is a system of equations on a manifold defined by equating to zero a number of exterior differential forms. When all the forms are linear, it is called a pfaffian system. Our object is to study its integral manifolds, i. e. , submanifolds satisfying all the equations of the system. A fundamental fact is that every equation implies the one obtained by exterior differentiation, so that the complete set of equations associated to an exterior differential system constitutes a differential ideal in the algebra of all smooth forms. Thus the theory is coordinate-free and computations typically have an algebraic character; however, even when coordinates are used in intermediate steps, the use of exterior algebra helps to efficiently guide the computations, and as a consequence the treatment adapts well to geometrical and physical problems. A system of partial differential equations, with any number of inde pendent and dependent variables and involving partial derivatives of any order, can be written as an exterior differential system. In this case we are interested in integral manifolds on which certain coordinates remain independent. The corresponding notion in exterior differential systems is the independence condition: certain pfaffian forms remain linearly indepen dent. Partial differential equations and exterior differential systems with an independence condition are essentially the same object.
Author:
Publisher:
ISBN:
Category : Aeronautics
Languages : en
Pages : 1148
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Book Description
Author: Kichoon Yang
Publisher: Springer Science & Business Media
ISBN: 9780792315933
Category : Mathematics
Languages : en
Pages : 214
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Book Description
This monograph presents a concise yet elementary account of exterior differential system theory so that it can be quickly applied to problems. The first part of the monograph, Chapters 1-5, deals with the general theory: the Cartan-Kaehler theorem is proved, the notions of involution and prolongation are carefully laid out, quasi-linear differential systems are examined in detail, and explicit examples of the Spencer cohomology groups and the characteristic variety are given. The second part of the monograph, Chapters 6 and 7, deals with applications to problems in differential geometry: the isometric embedding theorem of Cartan-Janet and its various geometric ramifications are discussed, a proof of the Andreotti-Hill theorem on the O-R embedding problem is given, and embeddings of abstract projective structures are discussed. For researchers and graduate students who would like a good introduction to exterior differential systems. This volume will also be particularly useful to those whose work involves differential geometry and partial differential equations.
Author:
Publisher:
ISBN:
Category : Science
Languages : en
Pages : 684
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Book Description
Author: Society for Industrial and Applied Mathematics
Publisher:
ISBN:
Category : Automatic control
Languages : en
Pages : 720
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Book Description
Author: Robert Bryant
Publisher: University of Chicago Press
ISBN: 9780226077932
Category : Mathematics
Languages : en
Pages : 230
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Book Description
In Exterior Differential Systems, the authors present the results of their ongoing development of a theory of the geometry of differential equations, focusing especially on Lagrangians and Poincaré-Cartan forms. They also cover certain aspects of the theory of exterior differential systems, which provides the language and techniques for the entire study. Because it plays a central role in uncovering geometric properties of differential equations, the method of equivalence is particularly emphasized. In addition, the authors discuss conformally invariant systems at length, including results on the classification and application of symmetries and conservation laws. The book also covers the Second Variation, Euler-Lagrange PDE systems, and higher-order conservation laws. This timely synthesis of partial differential equations and differential geometry will be of fundamental importance to both students and experienced researchers working in geometric analysis.
Author: Christopher I. Byrnes
Publisher: Springer Science & Business Media
ISBN: 1461241200
Category : Science
Languages : en
Pages : 444
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Book Description
The mathematical theory of networks and systems has a long, and rich history, with antecedents in circuit synthesis and the analysis, design and synthesis of actuators, sensors and active elements in both electrical and mechanical systems. Fundamental paradigms such as the state-space real ization of an input/output system, or the use of feedback to prescribe the behavior of a closed-loop system have proved to be as resilient to change as were the practitioners who used them. This volume celebrates the resiliency to change of the fundamental con cepts underlying the mathematical theory of networks and systems. The articles presented here are among those presented as plenary addresses, invited addresses and minisymposia presented at the 12th International Symposium on the Mathematical Theory of Networks and Systems, held in St. Louis, Missouri from June 24 - 28, 1996. Incorporating models and methods drawn from biology, computing, materials science and math ematics, these articles have been written by leading researchers who are on the vanguard of the development of systems, control and estimation for the next century, as evidenced by the application of new methodologies in distributed parameter systems, linear nonlinear systems and stochastic sys tems for solving problems in areas such as aircraft design, circuit simulation, imaging, speech synthesis and visionics.
Author: Heinz D. Unbehauen
Publisher: EOLSS Publications
ISBN: 1848261527
Category :
Languages : en
Pages : 516
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Book Description
This Encyclopedia of Control Systems, Robotics, and Automation is a component of the global Encyclopedia of Life Support Systems EOLSS, which is an integrated compendium of twenty one Encyclopedias. This 22-volume set contains 240 chapters, each of size 5000-30000 words, with perspectives, applications and extensive illustrations. It is the only publication of its kind carrying state-of-the-art knowledge in the fields of Control Systems, Robotics, and Automation and is aimed, by virtue of the several applications, at the following five major target audiences: University and College Students, Educators, Professional Practitioners, Research Personnel and Policy Analysts, Managers, and Decision Makers and NGOs.
