Abstract
This paper derives a field implicit Lagrangian system and a field implicit Euler-Lagrange equation. Field implicit Lagrangian systems are a global representation for higher order field equations derived from degenerate Lagrangians. Field implicit Euler-Lagrange equations are the local representation of field implicit Lagrangian systems. First, we derive the field implicit Lagrangian system under zero boundary conditions by using a Dirac differential. Next, we extend the field implicit Lagrangian system to the case of non-zero boundary conditions by using a Stokes-Dirac differential. A Stokes-Dirac differential is an extended Dirac differential in terms of integration by parts formula and Stokes theorem. Furthermore, we derive field implicit Euler-Lagrange equations from the Hamilton-Pontryagin principle.
