Abstract
Fundamental analytic, algebraic, and geometric properties of generalized Hamiltonian (Birkhoffian) theory are compared with the properties of a covering unitary phase-space formulation based on complex variables of the form (p+iq). Technical advantages in the unitary phase-space formulation are illustrated by a detailed discussion of the one-dimensional extended damped harmonic oscillator. One advantage is the ability to fully describe nonconservative constraint forces within a globally conservative system. Another advantage is that wider classes of gauge transformations are available to simplify the construction of smooth solution manifolds.
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References
R. Abraham and J. E. Marsden,Foundations of Mechanics (Benjamin/Cummings, Menlo Park, California, 1978).
V. I. Arnold, ed.,Dynamical Systems III (Springer, Berlin, 1985).
E. C. G. Südershan and N. Mukunda,Classical Mechanics: A Modern Perspective (Wiley, New York, 1974).
M. Santilli,Foundations of Theoretical Mechanics I, II (Springer, Berlin, 1978, 1983).
E. T. Abou El Dahab, “Unitary Space Formulation of Generalized Hamiltonian (Birkhoffian) Theory” (Ph.D. Thesis, University of Kent).
E. T. Abou El Dahab, J. S. R. Chisholm, and J. McEwan, “A Complex Formulation of Hamiltonian (or Birkhoffian) Theory,” to be published inClassical and Quantum Systems—Foundations and Symmetries (World Scientific, Singapore, 1992).
V. I. Arnold,Ordinary Differential Equations (MIT Press, Cambridge, Massachusetts, 1973).
P. M. Morse and H. Feshbach,Methods of Theoretical Physics (McGraw-Hill, New York, 1953).
A. O. Barut,Found. Theor. Phys. 17(6), 549 (1987).
W. H. Greub, Linear Algebra (Springer, Berlin, 1967).
A. O. Barut and J. McEwan,Lett. Math. Phys. 11, 67 (1986).
S. L. Adler, inNiels Bohr, Physics and the World: Proceedings of Niels Bohr Centennial Symposium, Hermann Feshbach, eds. (Harwood Publications, New York, 1988), pp. 213–229.
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McEwan, J. A complex formulation of generalized Hamiltonian (Birkhoffian) theory. Found Phys 23, 313–327 (1993). https://doi.org/10.1007/BF01883632
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DOI: https://doi.org/10.1007/BF01883632