Even More Generalized Hamiltonian Dynamics

TL;DR

This paper introduces Flannery brackets, a generalization of Poisson brackets, enabling derivation of classical equations of motion for systems with complex constraints, and explores their potential role in quantization procedures.

Contribution

It presents a new variational approach using Flannery brackets to handle non-holonomic constraints in Hamiltonian dynamics, extending classical methods.

Findings

Defined Flannery brackets as a generalization of Poisson brackets.

Derived equations of motion for constrained systems using the new brackets.

Proposed potential application of Flannery brackets in quantization of constrained systems.

Abstract

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.