Calculus of VariationsElements 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 Limited preview - 2000 |
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a₁ action admissible curves AJ[h arbitrary boundary conditions calculate calculus of variations canonical conditions y(a conjugate point consider const contains no points corresponding defined denote derivatives differential equation ditions dx dy end points Euler equations extremal extremum fact field formula func function y(x functional J[y given Hamilton-Jacobi equation hence 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 proved Qh² quadratic form quadratic functional second variation sequence solution strong extremum sufficient conditions surface system of Euler tangent Taylor's theorem theorem tion trajectories transformation vanishes variables variational problem vector x₁ y₁ zero θε Ән ди ду дук дх дхо Уп