Published

2009-01-01

Una Aplicación de las Series de Lie en el estudio del Problema de los Dos Cuerpos clásico

Keywords:

Series de Lie, problema de los dos cuerpos, mecánica celeste. (es)
Lie series, two-body problem, Celestial Mechanics. (en)

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Authors

  • J G Portilla B. Observatorio Astronómico Nacional, Facultad de Ciencias, Universidad Nacional de Colombia
  • E Brieva B. Escuela Colombiana de Ingeniería Julio Garavito
El clásico problema de dos cuerpos es analizado por series de Lie a través de una regularización común. Se muestra que por un cambio adecuado de la variable independiente (la introducción de un pseudo-tiempo) es posible obtener seis ecuaciones diferenciales que, integradas por series de Lie, dan expresiones cortas para los componentes de los vectores posición y velocidad. En principio, las expresiones son válidas para las cónicas y el movimiento rectilíneo.

The classical two-body problem is analyzed by Lie series through a common regularization. It is showed that by an appropriate change of the independent variable (introducing a pseudo-time) is possible to obtain six differential equations which, integrated by Lie series, give short expressions for the components of the position and velocity vectors. In principle, the expressions are valid for the conics and the rectilinear motion.

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