Abstract
This chapter may be considered a heuristic introduction and examination of the basic notions of the dynamical theory. For readers wishing to explore the equations of motion more directly at this point, it might be more appropriate to proceed to Chapter 5 and to use this chapter as a reference for certain features of the dynamical theory.
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References
J. R. Fanchi, Parameterized Relativistic Quantum Theory ( Kluwer Academic Press, Dordrecht, 1993 ).
That is, the invariant work function; see Section 1.4.
It is convenient to use the singular observer when referring to the existence of a class of observers related by trivial transformations with regard to the implied symmetry.
See, e. g., H. Goldstein, Classical Mechanics (Addison-Wesley, Reading, Mass., 2nd ed. 1980 ).
The stellar dynamics of the Galaxy are modeled to high order by a Newtonian gravitational potential, and thus it is possible to define a global inertial frame for the system; see J. Binney and S. Tremaine, Galactic Dynamics (Princeton Univ. Press, Princeton, N. J., 1987 ).
As discussed in Section 3.3, the fact that the representation (4.6) in terms of r is arbitrary does not imply that the parameter is chosen arbitrarily; see M. Lipschutz, Theory and Problems of Differential Geometry (McGraw-Hill, N. Y.,1969). The erroneous conclusion that because r is not the arc length, it must therefore be an arbitrary choice of parameter is responsible for the “vanishing Hamiltonian” problem discussed in A. O. Barut, Electrodynamics and Classical Theory of Fields and Particles ( Macmillan, N. Y., 1964 ).
A. J. Lichtenberg and M. A. Liebermann, Regular and Stochastic Motion ( Springer-Verlag, N. Y., 1981 ).
C.M. Lockhart, B. Misra, and I. Prigogine, Phys. Rev. D 25, 921 (1982). 17L. P. Horwitz, S. Shashoua, and W. C. Schieve, Physica A 161, 299 (1989).
J. L. Synge, Relativity: The Special Theory (North-Holland, Amsterdam, 2nd ed. 1965). This method of interaction is also assumed in fig. 1 of J. L. Cook, Aust. J. Phys. 25, 117 (1972). Cook, however, actually uses several methods of interaction within the same work, and some of his results are derived from the dynamical theory presented in this work. See Appendix B.
Moreover, it is the Minkowski arc length that is used as the common parameter.
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Trump, M.A., Schieve, W.C. (1999). The Dynamical Theory. In: Classical Relativistic Many-Body Dynamics. Fundamental Theories of Physics, vol 103. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9303-8_4
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DOI: https://doi.org/10.1007/978-94-015-9303-8_4
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