  After recalling standard nonlinear port-Hamiltonian systems and their
algebraic constraint equations, called here Dirac algebraic constraints, an
extended class of port-Hamiltonian systems is introduced. This is based on
replacing the Hamiltonian function by a general Lagrangian submanifold of the
cotangent bundle of the state space manifold, motivated by developments in
Barbero-Linan et al., and extending the linear theory as developed in Van der
Schaft et al., Beattie et al.. The resulting new type of algebraic constraints
equations are called Lagrange constraints. It is shown how Dirac algebraic
constraints can be converted into Lagrange algebraic constraints by the
introduction of extra state variables, and, conversely, how Lagrange algebraic
constraints can be converted into Dirac algebraic constraints by the use of
Morse families.
