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Exterior Differential Systems and the Calculus of Variations

Griffiths, Phillip;Griffiths, P.

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ISBN 10: 3764331038 / ISBN 13: 9783764331030
Published by Birkhauser, Secaucus, New Jersey, U.S.A., 1982
Condition: As New Hardcover
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This is a fine, as new, hardcover first edition copy, slick green binding, no DJ. Progress in mathematics, volume 25. Bookseller Inventory # 057821

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Bibliographic Details

Title: Exterior Differential Systems and the ...

Publisher: Birkhauser, Secaucus, New Jersey, U.S.A.

Publication Date: 1982

Binding: Hard Cover

Book Condition:As New

Dust Jacket Condition: No DJ

Edition: First Edition

About this title

Synopsis:

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.

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