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Hamiltonian Two-Body System in Special Relativity

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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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Authors and Affiliations

  1. Observatoire de Paris, CNRS, Université Paris Diderot, 5 place Jules Janssen, 92195, Meudon, France

    Philippe Droz-Vincent

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  1. Philippe Droz-Vincent
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Correspondence to Philippe Droz-Vincent.

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Droz-Vincent, P. Hamiltonian Two-Body System in Special Relativity. Int J Theor Phys 50, 3481–3502 (2011). https://doi.org/10.1007/s10773-011-0856-1

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  • DOI: https://doi.org/10.1007/s10773-011-0856-1

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