Hamiltonian Two-Body System in Special Relativity |
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Authors: | Philippe Droz-Vincent |
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Institution: | (1) Department Physics & Astronomy, University of Southern California, College of Letters, Arts & Sciences, Los Angeles, CA 90089-0484, USA;(2) Department Physics, University of California, Davis, Davis, CA 95616, USA |
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Abstract: | We consider an isolated system made of two pointlike bodies interacting at a distance in the nonradiative approximation. Our
framework is the covariant and a priori Hamiltonian formalism of “predictive relativistic mechanics”, founded on the equal-time condition. The center of mass is
rather a center of energy. Individual energies are separately conserved and the meaning of their positivity is discussed in
terms of world-lines. Several results derived decades ago under restrictive assumptions are extended to the general case.
Relative motion has a structure similar to that of a nonrelativistic one-body motion in a stationary external potential, but
its evolution parameter is generally not a linear function of the center-of-mass time, unless the relative motion is circular
(in this latter case the motion is periodic in the center-of-mass time). Finally the case of an extreme mass ratio is investigated.
When this ratio tends to zero the heavy body coincides with the center of mass provided that a certain first integral, related
to the binding energy, is not too large. |
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