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BL
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620016
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dltt
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| Main Entry
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Griffiths, Phillip A.
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| Title & Author
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Exterior Differential Systems and the Calculus of Variations\ by Phillip A. Griffiths.
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| Publication Statement
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Boston, MA :: Birkhäuser Boston :: Imprint: Birkhäuser,, 1983.
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| Series Statement
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Progress in Mathematics ;; 25
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| ISBN
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9781461581666
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: 9780817631031
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| Contents
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0. Preliminaries -- I. Euler-Lagrange Equations for Differential Systems with One Independent Variable -- II. First Integrals of the Euler-Lagrange System; Noether's Theorem and Examples -- III. Euler Equations for Variational Problems in Homogeneous Spaces -- IV. Endpoint Conditions; Jacobi Equations and the 2nd Variation; Conjugate Points; Fields and the Hamilton-Jacobi Equation; the Lagrange Problem -- Appendix: Miscellaneous Remarks and Examples -- a) Problems with Integral Constraints; Examples -- b) Classical Problems Expressed in Moving Frames.
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| Abstract
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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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| Subject
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Mathematics.
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Differentiable dynamical systems.
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Mathematical optimization.
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| Added Entry
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SpringerLink (Online service)
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