Synopsis
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.
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