Exterior Differential Systems & the Calculus of Variations: 25 - Rilegato

Griffiths, P.A.

Rilegato

ISBN 10: 0817631038 ISBN 13: 9780817631031

Casa editrice: Birkhäuser, 1983

Riassunto

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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Contenuti

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.

Dettagli dell'edizione

• Editore: Birkhäuser
• Data di pubblicazione: 1983
• Lingua: Inglese
• ISBN 10: 0817631038
• ISBN 13: 9780817631031
• Rilegatura: Copertina rigida
• Numero edizione: 1
• Numero di pagine: 352
• Contatto del produttore: non disponibile
• Persona responsabile: Springer Nature Customer Service Center GmbH; ProductSafety@springernature.com; ; Europaplatz 3,69115 Heidelberg, Germany; Heidelberg; 69115; Germania