ZM theory II: Hamilton's and Lagrange's equations of motion

We show that considering time measured by an observer to be a function of a cyclical field (an abstract version of a clock) is consistent with Hamilton's and Lagrange's equations of motion for a one dimensional space manifold. The derivation may provide a simple understanding of the conventions that are used in defining the relationship between independent and dependent variables in the Lagrangian and Hamiltonian formalisms. These derivations of the underlying principles of classical mechanics are steps on the way to discussions of physical laws and interactions in ZM theory.