Abstract
Relativistic speeds turn motion into an inherently many-body problem. But most motion at the human and planetary scale is not relativistic and therefore not inherently many-body. Solar system motions of macroscopic bodies including the atmosphere and oceans of a planet like the earth are well described nonrelativistically according to the mechanics of Galilean relativity. At the scale of the atom, the orbital speed of an electron is only a small fraction of the speed of light. The states of the hydrogen atom are well predicted by the nonrelativistic laws of quantum motion.
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References
Poincaré, H., Les Methods nouvelles de la méchanicque céleste, vols. 1–3, Gauthiers-Villars, Paris (1892–99); also available as a reprint from Dover Books, New York (1957). Poincaré’s method has come to be formalized as canonical perturbation theory and is presented in standard works, for example, Chapter 2 of A. J. Lichtenberg and M. A. Lieberman, Regular and Chaotic Dynamics, New York: Springer-Verlag, 1992.
For a more extended discussion of the KAM theory, see Chapter 5 of Florin Diacu and Philip Holmes, Celestial Encounters: The Origins of Chaos and Stability, Princeton: Princeton University Press, 1996.
See “Secular Perturbation Theory” in Chapter 2 of A. J. Lichtenberg and M. A. Lieberman, Regular and Chaotic Dynamics, New York: Springer-Verlag, 1992.
For a more thorough discussion of homoclinic orbits and chaotic motion in general, see J. Guckenheimer and P. J. Holmes Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields. Applied Mathematical Science No. 42, New York, Heidelberg, Berlin: Springer Verlag, 1983.
Wisdom, J., “Chaotic Dynamics of the Solar System,” ICARUS, 72, 241–275, 1987.
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(2004). The Manifold Universe. In: The Shaggy Steed of Physics. Springer, New York, NY. https://doi.org/10.1007/978-0-387-21806-9_7
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DOI: https://doi.org/10.1007/978-0-387-21806-9_7
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