Even More Generalized Hamiltonian Dynamics

We establish the procedure to derive from an action-based variational principle the classical equations of motion in Hamiltonian phase space of a particle subject to general position and velocity dependent non-holonomic equality constraints. Key to the procedure is our introduction of Flannery brackets, which generalize Poisson brackets. We conjecture on some implications, including the possibility of replacing Poisson brackets with Flannery brackets in Dirac's brackets to provide the quantization procedure for general non-holonomic equality constraint systems.