dor_id: 40988

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100.1.#.a: Lonngi, P.; Piña, E.

524.#.#.a: Lonngi, P., et al. (2003). On the figure eight orbit of the three-body problem. Revista Mexicana de Física; Vol 49, No 005. Recuperado de https://repositorio.unam.mx/contenidos/40988

245.1.0.a: On the figure eight orbit of the three-body problem

502.#.#.c: Universidad Nacional Autónoma de México

561.1.#.a: Facultad de Ciencias, UNAM

264.#.0.c: 2003

264.#.1.c: 2003-01-01

653.#.#.a: Three-body problem; zero angular momentum; equal-mass case; figure-eight orbit; Jacobi’s action

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884.#.#.k: http://revistas.unam.mx/index.php/rmf/article/view/13920

041.#.7.h: eng

520.3.#.a: A new solution to the three-body problem interacting through gravitational forces with equal masses and zero angular momentum, has been recently discovered. This is a periodic symmetric orbit where the particles follow a figure eight trajectory in the plane. They alternate between six isosceles-aligned positions and six isosceles triangle positions in a periodic orbit composed by twelve equivalent segments. The condition of zero angular momentum is considered assuming that the three masses can be equal or different, yielding in both cases the same final expression for the kinetic energy. We found that the property of this orbit of having isosceles configurations, is a general feature to be found in any orbit of the equal-mass case, associated with an increase of π/6 in one angle of our set of coordinates. The figure-eight solution is determined by expanding two of our coordinates in a Fourier series of that angle, by using the Jacobi-Maupertuis principle as opposed to the standard Lagrangian action. The time and the angle conjugated to the angular momentum are also expressed in terms of that same angle.

773.1.#.t: Revista Mexicana de Física; Vol 49, No 005 (2003)

773.1.#.o: http://revistas.unam.mx/index.php/rmf

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Artículo

On the figure eight orbit of the three-body problem

Lonngi, P.; Piña, E.

Facultad de Ciencias, UNAM, publicado en Revista Mexicana de Física, y cosechado de Revistas UNAM

Licencia de uso

Procedencia del contenido

Entidad o dependencia
Facultad de Ciencias, UNAM
Revista
Repositorio
Contacto
Revistas UNAM. Dirección General de Publicaciones y Fomento Editorial, UNAM en revistas@unam.mx

Cita

Lonngi, P., et al. (2003). On the figure eight orbit of the three-body problem. Revista Mexicana de Física; Vol 49, No 005. Recuperado de https://repositorio.unam.mx/contenidos/40988

Descripción del recurso

Autor(es)
Lonngi, P.; Piña, E.
Tipo
Artículo de Investigación
Área del conocimiento
Físico Matemáticas y Ciencias de la Tierra
Título
On the figure eight orbit of the three-body problem
Fecha
2003-01-01
Resumen
A new solution to the three-body problem interacting through gravitational forces with equal masses and zero angular momentum, has been recently discovered. This is a periodic symmetric orbit where the particles follow a figure eight trajectory in the plane. They alternate between six isosceles-aligned positions and six isosceles triangle positions in a periodic orbit composed by twelve equivalent segments. The condition of zero angular momentum is considered assuming that the three masses can be equal or different, yielding in both cases the same final expression for the kinetic energy. We found that the property of this orbit of having isosceles configurations, is a general feature to be found in any orbit of the equal-mass case, associated with an increase of π/6 in one angle of our set of coordinates. The figure-eight solution is determined by expanding two of our coordinates in a Fourier series of that angle, by using the Jacobi-Maupertuis principle as opposed to the standard Lagrangian action. The time and the angle conjugated to the angular momentum are also expressed in terms of that same angle.
Tema
Three-body problem; zero angular momentum; equal-mass case; figure-eight orbit; Jacobi’s action
Idioma
eng
ISSN
2683-2224 (digital); 0035-001X (impresa)

Enlaces