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Field name	Details
Dewey Class	515.64
Title	Exterior Differential Systems and the Calculus of Variations ([EBook]) / by Phillip A. Griffiths.
Author	Griffiths, Phillip A. , 1938-
Other name(s)	SpringerLink (Online service)
Publication	Boston, MA : Birkhäuser , 1983.
Physical Details	IX, 339 pages : online resource.
Series	Progress in mathematics 0743-1643 ; ; 25
ISBN	9781461581666
Summary 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.:
Contents 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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-1-4615-8166-6
Links to Related Works	Subject References: Calculus of variations . Calculus of variations and optimal control; optimization . Dynamical systems and ergodic theory . Dynamics . Ergodic theory . Authors: Griffiths, Phillip A. 1938- . Griffiths, Phillip A., 1938- . Corporate Authors: SpringerLink (Online service) . Series: Progress in mathematics . Classification: 515.64 .

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Exterior Differential Systems and the Calculus of Variations

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