Exterior Differential Systems and the Calculus of Variations / by Phillip A. Griffiths
(Progress in Mathematics ; 25)
| データ種別 | 電子ブック |
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| 出版情報 | Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser , 1983 |
| 本文言語 | 英語 |
| 大きさ | IX, 339 p : online resource |
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| 内容注記 | 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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| 一般注記 | 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 |
| 著者標目 | *Griffiths, Phillip A. author SpringerLink (Online service) |
| 件 名 | LCSH:Mathematics LCSH:Dynamics LCSH:Ergodic theory LCSH:Calculus of variations FREE:Mathematics FREE:Calculus of Variations and Optimal Control; Optimization FREE:Dynamical Systems and Ergodic Theory |
| 分 類 | DC23:515.64 |
| 巻冊次 | ISBN:9781461581666 
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| ISBN | 9781461581666 |
| URL | http://dx.doi.org/10.1007/978-1-4615-8166-6 |
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