A scheme for generating variational principles for a given system of ODE or PDE with algebraic constraints will be described. It is well known that many physically relevant governing equations, whether time dependent or independent, do not arise from a variational principle. A corresponding variational principle can be useful for purposes of analysis or computation. The development of a family of convex 'dual' variational principles for systems of 'primal' equations with the property that the Euler-Lagrange system of each of its members is the primal system in a well-defined sense will be described. The scheme has many interesting properties, like converting a primal hyperbolic system to a degenerate-elliptic dual problem in space-time domains. The idea has been demonstrated through computation on Euler's system of ODE for the motion of a rigid body about a fixed point, the heat equation, the inviscid Burgers equation, traveling waves for a dispersive, non-local, semidiscrete Burgers equation, and (unregularized) nonconvex elastodynamics in 1-d x time.

Some of these results will be discussed, and rigorous results obtained with the scheme so far will be sketched.

This is joint work with Janusz Ginster, Uditnarayan Kouskiya, Bob Pego, Siddharth Singh, and Dmitry Vorotnikov.