Exterior Differential Systems And The Calculus Of Variations
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Exterior Differential Systems And The Calculus Of Variations
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Author : P.A. Griffiths
language : en
Publisher: Birkhäuser
Release Date : 2013-05-16
Exterior Differential Systems And The Calculus Of Variations written by P.A. Griffiths and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-05-16 with Mathematics categories.
15 0. PRELIMINARIES a) Notations from Manifold Theory b) The Language of Jet Manifolds c) Frame Manifolds d) Differentia! Ideals e) Exterior Differential Systems EULER-LAGRANGE EQUATIONS FOR DIFFERENTIAL SYSTEMS ~liTH ONE I. 32 INDEPENDENT VARIABLE a) Setting up the Problem; Classical Examples b) Variational Equations for Integral Manifolds of Differential Systems c) Differential Systems in Good Form; the Derived Flag, Cauchy Characteristics, and Prolongation of Exterior Differential Systems d) Derivation of the Euler-Lagrange Equations; Examples e) The Euler-Lagrange Differential System; Non-Degenerate Variational Problems; Examples FIRST INTEGRALS OF THE EULER-LAGRANGE SYSTEM; NOETHER'S II. 1D7 THEOREM AND EXAMPLES a) First Integrals and Noether's Theorem; Some Classical Examples; Variational Problems Algebraically Integrable by Quadratures b) Investigation of the Euler-Lagrange System for Some Differential-Geometric Variational Pro~lems: 2 i) ( K ds for Plane Curves; i i) Affine Arclength; 2 iii) f K ds for Space Curves; and iv) Delauney Problem. II I. EULER EQUATIONS FOR VARIATIONAL PROBLEfiJS IN HOMOGENEOUS SPACES 161 a) Derivation of the Equations: i) Motivation; i i) Review of the Classical Case; iii) the Genera 1 Euler Equations 2 K /2 ds b) Examples: i) the Euler Equations Associated to f for lEn; but for Curves in i i) Some Problems as in i) sn; Non- Curves in iii) Euler Equations Associated to degenerate Ruled Surfaces IV.
Exterior Differential Systems And The Calculus Of Variations
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Author : Phillip Griffiths
language : en
Publisher: Birkhauser
Release Date : 1983
Exterior Differential Systems And The Calculus Of Variations written by Phillip Griffiths and has been published by Birkhauser this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with Mathematics categories.
Exterior Differential Systems
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Author : Robert L. Bryant
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Exterior Differential Systems written by Robert L. Bryant and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.
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.
Proceedings Of The Sixth International Colloquium On Differential Equations
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Author : Dimitūr Baīnov
language : en
Publisher: VSP
Release Date : 1996-01-01
Proceedings Of The Sixth International Colloquium On Differential Equations written by Dimitūr Baīnov and has been published by VSP this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-01-01 with Mathematics categories.
The Sixth International Colloquium on Differential Equations was organized by the Institute for Basic Science of Inha University, the International Federation of Nonlinear Analysts, the Mathematical Society of Japan, the Pharmaceutical Faculty of the Medical University of Sofia, the University of Catania, and UNESCO, with the cooperation of a number of international mathematical organizations, and was held at the Technical University of Plovdiv, Bulgaria, from 18 to 23 August 1995. This proceedings volume contains selected talks which deal with various aspects of differential and partial differential equations.
Exterior Differential Systems And Euler Lagrange Partial Differential Equations
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Author : Robert Bryant
language : en
Publisher: University of Chicago Press
Release Date : 2003-07
Exterior Differential Systems And Euler Lagrange Partial Differential Equations written by Robert Bryant and has been published by University of Chicago Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-07 with Mathematics categories.
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.
The Geometry Of Ordinary Variational Equations
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Author : Olga Krupkova
language : en
Publisher: Springer
Release Date : 2006-11-14
The Geometry Of Ordinary Variational Equations written by Olga Krupkova and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
The book provides a comprehensive theory of ODE which come as Euler-Lagrange equations from generally higher-order Lagrangians. Emphasis is laid on applying methods from differential geometry (fibered manifolds and their jet-prolongations) and global analysis (distributions and exterior differential systems). Lagrangian and Hamiltonian dynamics, Hamilton-Jacobi theory, etc., for any Lagrangian system of any order are presented. The key idea - to build up these theories as related with the class of equivalent Lagrangians - distinguishes this book from other texts on higher-order mechanics. The reader should be familiar with elements of differential geometry, global analysis and the calculus of variations.
Essays On Mathematical Robotics
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Author : John Baillieul
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Essays On Mathematical Robotics written by John Baillieul and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The chapters in this book present an excellent exposition of recent developments in both robotics and nonlinear control centering around "hyper-redundancy", highly oscillatory inputs, optimal control, exterior differential systems, and the use of generic loops. The principal topics covered in the book are: adaptive control for a class of nonlinear systems, event-based motion planning, nonlinear control synthesis and path planning in robotics with special emphasis on nonholonomic and "hyper-redundant" robotic systems, control design and stabilization of driftless affine control systems (of the type arising in the kinematic control of nonholonomic robotic systems), control design methods for Hamiltonian systems and exterior differential systems. The chapter covering exterior differential systems contains a detailed introduction to the use of exterior differential methods, including the Goursat and extended Goursat normal forms and their application to path planning for nonholonomic systems.
Real And Complex Submanifolds
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Author : Young Jin Suh
language : en
Publisher: Springer
Release Date : 2014-12-05
Real And Complex Submanifolds written by Young Jin Suh and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-05 with Mathematics categories.
Edited in collaboration with the Grassmann Research Group, this book contains many important articles delivered at the ICM 2014 Satellite Conference and the 18th International Workshop on Real and Complex Submanifolds, which was held at the National Institute for Mathematical Sciences, Daejeon, Republic of Korea, August 10–12, 2014. The book covers various aspects of differential geometry focused on submanifolds, symmetric spaces, Riemannian and Lorentzian manifolds, and Kähler and Grassmann manifolds.
Clifford Algebras And Their Applications In Mathematical Physics
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Author : Rafal Ablamowicz
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Clifford Algebras And Their Applications In Mathematical Physics written by Rafal Ablamowicz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The plausible relativistic physical variables describing a spinning, charged and massive particle are, besides the charge itself, its Minkowski (four) po sition X, its relativistic linear (four) momentum P and also its so-called Lorentz (four) angular momentum E # 0, the latter forming four trans lation invariant part of its total angular (four) momentum M. Expressing these variables in terms of Poincare covariant real valued functions defined on an extended relativistic phase space [2, 7J means that the mutual Pois son bracket relations among the total angular momentum functions Mab and the linear momentum functions pa have to represent the commutation relations of the Poincare algebra. On any such an extended relativistic phase space, as shown by Zakrzewski [2, 7], the (natural?) Poisson bracket relations (1. 1) imply that for the splitting of the total angular momentum into its orbital and its spin part (1. 2) one necessarily obtains (1. 3) On the other hand it is always possible to shift (translate) the commuting (see (1. 1)) four position xa by a four vector ~Xa (1. 4) so that the total angular four momentum splits instead into a new orbital and a new (Pauli-Lubanski) spin part (1. 5) in such a way that (1. 6) However, as proved by Zakrzewski [2, 7J, the so-defined new shifted four a position functions X must fulfill the following Poisson bracket relations: (1.
Sixth Marcel Grossmann Meeting The On Recent Developments In Theoretical And Experimental General Relativity Gravitation And Relativistic Field Theories In 2 Volumes
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Author : Humitaka Sato
language : en
Publisher: World Scientific
Release Date : 1993-01-08
Sixth Marcel Grossmann Meeting The On Recent Developments In Theoretical And Experimental General Relativity Gravitation And Relativistic Field Theories In 2 Volumes written by Humitaka Sato and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-01-08 with categories.
The Marcel Grossmann Meetings have been conceived with the aim of reviewing recent advances in gravitation and general relativity, with particular emphasis on mathematical foundations and physical predictions. The overall programme includes the broad categories of mathematical techniques, cosmology, quantum gravity, astrophysics, gravitational radiation and experimental developments.The proceedings contain invited and contributed papers.