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Journal Articles International Journal of Theoretical Physics Year : 2011

Hamiltonian Two-Body System in Special Relativity


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.

Dates and versions

hal-03742310 , version 1 (02-08-2022)



Philippe Droz-Vincent. Hamiltonian Two-Body System in Special Relativity. International Journal of Theoretical Physics, 2011, 50, pp.3481-3502. ⟨10.1007/s10773-011-0856-1⟩. ⟨hal-03742310⟩
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