New coordinates for the four-body problem
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| Format: | Artículo científico |
| Langue: | en |
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Sociedad Mexicana de Física A.C.
2010
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| _version_ | 1876458878207524864 |
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| author | E. Piña |
| author_facet | E. Piña |
| contents | New coordinates for the four-body problem E. Piña Física, Astronomía y Matemáticas Four body problem new coordinates A new coordinate system is defined to study the physical Four-Body dynamical problem with general masses, with the origin the of coordinates at the center of mass. The transformation from the frame of inertial coordinates involves a combination of a rotation to the system of principal axis of inertia, followed by three changes of scale modifying the principal moments of inertia yield to a body with three equal moments of inertia, and finally a second rotation that leaves unaltered the equal moments of inertia. These three transformation steps yield a mass-dependent, rigid, orthocentric tetrahedron of constant volume in the baricentric inertial coordinates. Each of those three linear transformations is a function of three coordinates that produce the nine degrees of freedom of the Physical Four-Body problem, in a coordinate system with the center of mass as origin. The relation between the well-known equilateral tetrahedron solution to the gravitational Four-Body problem and the new coordinates is exhibited, and the planar case of central configurations with four different masses is computed numerically in these coordinates. 2010 artículo científico 0035-001X https://www.redalyc.org/articulo.oa?id=57019192002 en http://www.redalyc.org/revista.oa?id=570 Revista Mexicana de Física application/pdf Sociedad Mexicana de Física A.C. Revista Mexicana de Física (México) Num.3 Vol.56 |
| format | Artículo científico |
| id | redalyc_57019192002 |
| institution | Redalyc |
| language | en |
| publishDate | 2010 |
| publisher | Sociedad Mexicana de Física A.C. |
| spellingShingle | New coordinates for the four-body problem E. Piña Física, Astronomía y Matemáticas Four body problem new coordinates New coordinates for the four-body problem E. Piña Física, Astronomía y Matemáticas Four body problem new coordinates A new coordinate system is defined to study the physical Four-Body dynamical problem with general masses, with the origin the of coordinates at the center of mass. The transformation from the frame of inertial coordinates involves a combination of a rotation to the system of principal axis of inertia, followed by three changes of scale modifying the principal moments of inertia yield to a body with three equal moments of inertia, and finally a second rotation that leaves unaltered the equal moments of inertia. These three transformation steps yield a mass-dependent, rigid, orthocentric tetrahedron of constant volume in the baricentric inertial coordinates. Each of those three linear transformations is a function of three coordinates that produce the nine degrees of freedom of the Physical Four-Body problem, in a coordinate system with the center of mass as origin. The relation between the well-known equilateral tetrahedron solution to the gravitational Four-Body problem and the new coordinates is exhibited, and the planar case of central configurations with four different masses is computed numerically in these coordinates. 2010 artículo científico 0035-001X https://www.redalyc.org/articulo.oa?id=57019192002 en http://www.redalyc.org/revista.oa?id=570 Revista Mexicana de Física application/pdf Sociedad Mexicana de Física A.C. Revista Mexicana de Física (México) Num.3 Vol.56 |
| title | New coordinates for the four-body problem |
| topic | Física, Astronomía y Matemáticas Four body problem new coordinates |
| url | https://www.redalyc.org/articulo.oa?id=57019192002 |