Physical Sciences and Mathematics Commons^™

On The Existence Of Global Variational Principles, Ian M. Anderson, T. Duchamp

Mathematics and Statistics Faculty Publications

In studying physical phenomena one frequently encounters differential equations which arise from a variational principle, i.e. the equations are the Euler-Lagrangequations obtained from the fundamental (or action) integral of a problem in the calculus of variations. Because solutions to the Euler-Lagrange equations determine the possible extrema of the fundamental integral, the first step in the solution of a given problem in the calculus of variations is to obtain the appropriate Euler-Lagrange equations. This state of affairs suggests the so-called inverse problem, viz. does a given differential equation arise from a variational principle and, if so, what is the Lagrangian for …