Calculus of VariationsPrentice-Hall, 1963 - 232 sidor Elements of the theory -- Further generalizations -- The general variation of a functional -- The canonical form of the euler equations and related topics -- The second variation : sufficient conditions for a weak extremum -- Fields : sufficient conditions for a strong extremum -- Variational problems involving multiple integrals -- Direct methods in the calculus of variations -- Appendix I. Propagation of disturbances and the canonical equations -- Appendix II. Variational methods in problems of optimal control. |
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Calculus of Variations Izrail Moiseevitch Gelfand,Serge? Vasil?evich Fomin,Richard A. Silverman Begränsad förhandsgranskning - 2000 |
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admissible curves arbitrary boundary conditions calculate calculus of variations canonical conditions h(a conjugate point consider const contains no points corresponding defined denote derivatives differential equation ditions dx dy end points Euler equations extremal extremum F₁ fact field formula func function y(x functional J[y given h₁ Hamilton-Jacobi equation integral integrand interval invariant Jacobi lemma linear space matrix minimum necessary condition Noether's Theorem nonnegative obtain order higher P₁ parameter particle Ph'² points conjugate positive definite prob proved Qh² quadratic form quadratic functional second variation sequence solution strong extremum sufficient conditions surface system of Euler t₁ tangent Taylor's theorem theorem tion trajectories transformation U₁ vanishes variables variational problem vector x₁ y₁ y²² zero ән ди др ду дук дх