Revista UIS Ingenierías

Vol. 24 No. 1 (2025): Revista UIS Ingenierías
Articles

A brief solution to three-body problem: Newtonian and Hamiltonian versions

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  • Cristian Aguirre -Tellez,
  • Miryam Rincon-Joya,
  • José José Barba-Ortega
Cristian Aguirre -Tellez
Universidade Federal de Mato Groso
Miryam Rincon-Joya
Universidad Nacional de Colombia
José José Barba-Ortega
Universidad Nacional de Colombia
DOI: https://doi.org/10.18273/revuin.v24n1-2025004

Published 2025-03-05

Keywords

  • Toroidal geometry,
  • Maxwell's equations,
  • Numerical methods,
  • Hamiltonian,
  • Lagrangian

How to Cite

Aguirre -Tellez, C. ., Rincon-Joya, M., & Barba-Ortega, J. J. (2025). A brief solution to three-body problem: Newtonian and Hamiltonian versions. Revista UIS Ingenierías, 24(1), 37–44. https://doi.org/10.18273/revuin.v24n1-2025004

Copyright (c) 2025 Revista UIS Ingenierías

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Abstract

The problem of the three bodies was cataloged as one of the best-positioned problems and the pinnacle of functional analysis by Poincaré himself when he discovered that the problem itself presents a chaotic behavior and that it was impossible to apply integrable methods to this system. Therefore, its analytical solution was impossible to obtain, since its solution strongly depended on the initial conditions (weak chaos). With the development of modern numerical methods, together with the immense advances in the hardware of the new computers, attempts have been made to attack this system from different schemes and numerical stencils, to describe the main physical properties of this system (the trajectory is only one of these). With this, in the present work, we will study this problem from the Newtonian and Hamiltonian versions and the restricted problem. Special interest will be devoted to the numerical analysis of this system, The work focuses on a pedagogical description of the topic (constructivist), academic clarity, and application of numerical analysis.

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