Dynamics on Differential One-Forms
by
Troy L. Story
Morehouse College

Mathematical models of dynamics employing exterior calculus are shown to be mathematical representations of a unifying principle; namely, the description of a dynamic system with a characteristic differential one-form on an odd-dimensional differentiable manifold leads, by analysis with exterior calculus, to a set of characteristic differential equations and a characteristic tangent vector which define transformations of the system. This principle, whose origin is Arnold’s use of exterior calculus to describe Hamiltonian mechanics and geometric optics, is applied to irreversible thermodynamics and the dynamics of black holes, electromagnetism and strings. It is shown that “exterior calculus” models apply to systems for which the direction of change is given by a characteristic tangent vector and “conventional calculus” models apply to systems whose direction of change is arbitrary. The relationship between the two types of models is shown to imply a technical definition of dynamic equilibrium. J. Math. Chem. 29(2), 85-96 (2001).

Date received: February 28, 2003

Copyright © 2003 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cakr-87.