variational principle associated to a class of degenerate Lagrangians, whose degeneracy results from the action of the symmetry group. The defining feature of this principle is that the Lagrange multipliers are elements of the Lie algebra of the symmetry group and that they couple to the configuration variables via a given Lie algebra action. The resulting equations of motion, which we call the Clebsch–Euler–Lagrange equations, decompose into an evolution and a constraint equation. Next, we define a Clebsch–Legendre transformation similar to the ordinary Legendre transformation leading to what we call the Clebsch–Hamiltonian picture. As we will show, the constraints that arise from the degeneracy of the Lagrangian are phrased as momentum map constraints on the Hamiltonian side.

We then use the geometric formulation of the Dirac–Bergmann algorithm in the formulation of @GotayNesterHinds1978 to derive the Clebsch–Legendre transformation from an ordinary Legendre transformation of an extended Lagrangian system. In this process, we isolate two constraint equations, which are later given a geometric interpretation in terms of a symplectic reduction by stages procedure. This analysis of the constraints extends the well-known results for Yang–Mills theory [@BergveltDeKerf1986; @BergveltDeKerf1986a] and general relativity [@Giulini2015].

Since constraints which allow a reformulation in terms of symmetric Hamiltonian 