The Inverse Problem of the Calculus of Variations Local and Global Theory /

• Corporate Author: SpringerLink (Online service)
• Other Authors: Zenkov, Dmitry V. (Editor)
• Format: Electronic eBook
• Language: English
• Published: Paris : Atlantis Press : Imprint: Atlantis Press, 2015.
• Edition: 1st ed. 2015.
• Series: Atlantis Studies in Variational Geometry, 2
• Subjects: Mathematics.; Global analysis (Mathematics).; Manifolds (Mathematics).; Differential geometry.; Calculus of variations.; Gravitation.; Calculus of Variations and Optimal Control; Optimization.; Global Analysis and Analysis on Manifolds.; Differential Geometry.; Classical and Quantum Gravitation, Relativity Theory.

The aim of the present book is to give a systematic treatment of the inverse problem of the calculus of variations, i.e. how to recognize whether a system of differential equations can be treated as a system for extremals of a variational functional (the Euler-Lagrange equations), using contemporary...

Table of Contents:

• The Helmholtz Conditions and the Method of Controlled Lagrangians
• The Sonin–Douglas Problem
• Inverse Variational Problem and Symmetry in Action: The Relativistic Third Order Dynamics
• Variational Principles for Immersed Submanifolds
• Source Forms and their Variational Completions
• First-Order Variational Sequences in Field Theory.