Amb motiu del tancament d'estiu, la validació de documents es reprendrà a partir del 28 d'agost de 2026. Disculpeu les molèsties.
Con motivo del cierre de verano, la validación de documentos se reanudará a partir del 28 de agosto de 2026. Disculpad las molestias
Due to the summer closure, document validation will resume starting August 28, 2026. We apologize for any inconvenience.

Files

tfg_pablo_romero_marimon.pdf (681.72 KB)

Document type

Bachelor thesis

Publication date

2021-01-24

Publication license

cc-by-nc-nd (c) Pablo Romero Marimon, 2021
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/181696

On the stability of the Lagrangian points in the restricted circular 3-body problem

Journal Title

Authors

Director/Tutor

Journal ISSN

Volume Title

Related resource

Abstract

[en] The 3-body problem is one of the most celebrated problems in mathematics. In this work we aim to find the equilibrium points of one of the three masses, which is considered infinitesimal, and study their stability in two different phase spaces. The question of stability is addressed using both analytical and numerical methods. Whereas the Lyapunov and KAM theories provide us with analytical proofs of the stable or unstable behaviour in the first phase space, analytical methods motivated by the Nekhoroshev theory allow us to compute practical bounds of the time until which the infinitesimal mass remains near the equilibria in the second. Finally, these bounds are applied to the case of a well known system: the Sun-Jupiter-Trojan system.

Description

Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2021, Director: Àngel Jorba i Monte

Subject

Problema dels tres cossos, Treballs de fi de grau, Mecànica celeste, Sistemes hamiltonians, Anàlisi numèrica

Subject (English)

Three-body problem, Bachelor's theses, Celestial mechanics, Hamiltonian systems, Numerical analysis

Citation

Collections

Treballs Finals de Grau (TFG) - Matemàtiques

Citation

ROMERO MARIMON, Pablo. On the stability of the Lagrangian points in the restricted circular 3-body problem. [consulted: 15 of August of 2026]. Available at: https://hdl.handle.net/2445/181696

Export metadata

JSON - METS

Share record