Author	Griffiths, Phillip A. author
Title	Exterior Differential Systems and the Calculus of Variations [electronic resource] / by Phillip A. Griffiths
Imprint	Boston, MA : Birkhรคuser Boston : Imprint: Birkhรคuser, 1983
Connect to	http://dx.doi.org/10.1007/978-1-4615-8166-6
Descript	IX, 339 p. online resource

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 Prõlems: 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

0. Preliminaries -- I. Euler-Lagrange Equations for Differential Systems with One Independent Variable -- II. First Integrals of the Euler-Lagrange System; Noetherโs 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

1. Mathematics
2. Dynamics
3. Ergodic theory
4. Calculus of variations
5. Mathematics
6. Calculus of Variations and Optimal Control; Optimization
7. Dynamical Systems and Ergodic Theory