Mathematical Modeling of Constrained Hamiltonian Systems

Network modelling of unconstrained energy conserving physical systems leads to an intrinsic generalized Hamiltonian formulation of the dynamics. Constrained energy conserving physical systems are directly modelled as implicit Hamiltonian systems with regard to a generalized Dirac structure on the space of energy variables, which can be rewritten (under a nondegeneracy condition on the internal energy) as an explicit generalized Hamiltonian system on the constrained state space. This is specialized to mechanical systems with kinematic constraints.