A brief solution to three-body problem: Newtonian and Hamiltonian versions
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, i...
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Universidad Industrial de Santander
2025-03-01
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| Series: | Revista UIS Ingenierías |
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| Online Access: | https://revistas.uis.edu.co/index.php/revistauisingenierias/article/view/15793 |
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| author | Cristian Aguirre -Tellez Miryam Rincon-Joya José José Barba-Ortega |
| author_facet | Cristian Aguirre -Tellez Miryam Rincon-Joya José José Barba-Ortega |
| author_sort | Cristian Aguirre -Tellez |
| collection | DOAJ |
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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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| format | Article |
| id | doaj-art-d8e4848cf3484af3b8ad775d103edc39 |
| institution | DOAJ |
| issn | 1657-4583 2145-8456 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | Universidad Industrial de Santander |
| record_format | Article |
| series | Revista UIS Ingenierías |
| spelling | doaj-art-d8e4848cf3484af3b8ad775d103edc392025-08-20T02:59:46ZengUniversidad Industrial de SantanderRevista UIS Ingenierías1657-45832145-84562025-03-0124110.18273/revuin.v24n1-2025004A brief solution to three-body problem: Newtonian and Hamiltonian versionsCristian Aguirre -Tellez0Miryam Rincon-Joya1José José Barba-Ortega2Universidade Federal de Mato GrosoUniversidad Nacional de ColombiaUniversidad Nacional de Colombia 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. https://revistas.uis.edu.co/index.php/revistauisingenierias/article/view/15793Toroidal geometryMaxwell's equationsNumerical methodsHamiltonianLagrangian |
| spellingShingle | Cristian Aguirre -Tellez Miryam Rincon-Joya José José Barba-Ortega A brief solution to three-body problem: Newtonian and Hamiltonian versions Revista UIS Ingenierías Toroidal geometry Maxwell's equations Numerical methods Hamiltonian Lagrangian |
| title | A brief solution to three-body problem: Newtonian and Hamiltonian versions |
| title_full | A brief solution to three-body problem: Newtonian and Hamiltonian versions |
| title_fullStr | A brief solution to three-body problem: Newtonian and Hamiltonian versions |
| title_full_unstemmed | A brief solution to three-body problem: Newtonian and Hamiltonian versions |
| title_short | A brief solution to three-body problem: Newtonian and Hamiltonian versions |
| title_sort | brief solution to three body problem newtonian and hamiltonian versions |
| topic | Toroidal geometry Maxwell's equations Numerical methods Hamiltonian Lagrangian |
| url | https://revistas.uis.edu.co/index.php/revistauisingenierias/article/view/15793 |
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