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Tensor-product representation of Laplace-Runge-Lenz vector for two-body Kepler systems

  • Mathematics
  • Published:
Wuhan University Journal of Natural Sciences

Abstract

A unified tensor-product representation of Laplace-Runge-Lenz (LRL) vector about inversely-quadric and centric-force systems is derived. For a two-body Kepler system under gravitation or Coulomb force, the modified and unified tensor- product representation of LRL vector is also deduced by using an effective single-body description. Some properties of the vector are numerated and proved. Conservation of this vector is demonstrated in the tensor-product form. The energy formula for a bound-state elliptic orbit is simply derived via a novel approach. For a two-body system, the R-test rules for every kinds of Kepler’s motion are discussed in detail.

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Authors and Affiliations

  1. School of Physics and Technology, Wuhan University, Wuhan 430072, Hubei, China

    Guoquan Zhou

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  1. Guoquan Zhou
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Correspondence to Guoquan Zhou.

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Foundation item: Supported by the National Teaching Team Foundation (202276003)

Biography: ZHOU Guoquan, male, Ph.D., Associate professor, research direction: nonlinear integrable equations and field theory.

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Zhou, G. Tensor-product representation of Laplace-Runge-Lenz vector for two-body Kepler systems. Wuhan Univ. J. Nat. Sci. 22, 51–56 (2017). https://doi.org/10.1007/s11859-017-1215-8

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  • DOI: https://doi.org/10.1007/s11859-017-1215-8

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