عنوان

Exterior Differential Systems and the Calculus of Variations

(Number (ISBN

9780817631031

(Number (ISBN

9781461581666

Number

dltt

Title Proper

Exterior Differential Systems and the Calculus of Variations

General Material Designation

[Book]

First Statement of Responsibility

by Phillip A. Griffiths.

Place of Publication, Distribution, etc.

Boston, MA :

Name of Publisher, Distributor, etc.

Imprint: Birkhäuser,

Date of Publication, Distribution, etc.

1983.

Series Title

Progress in Mathematics ;

Volume Designation

25

Text of Note

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.

0

Text of Note

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.

International Standard Book Number

9780817631031

Title

Springer eBooks

Differentiable dynamical systems.

Mathematical optimization.

Mathematics.

Griffiths, Phillip A.

SpringerLink (Online service)

Date of Transaction

20190301081800.0

Electronic name

[Book]

Y