EL PROBLEMA RESTRINGIDO DE LOS TRES CUERPOS POR SERIES DE LIE

José Gregorio Portilla

doi:10.18257/raccefyn.27(103).2003.2059

Vol. 27 No. 103 (2003), Physical Sciences

Vol. 27 No. 103 (2003)

THE RESTRICTED THREE BODY PROBLEM BY LIE SERIES.

Physical Sciences

https://doi.org/10.18257/raccefyn.27(103).2003.2059

Published 2023-10-10

José Gregorio Portilla⁺⁻

José Gregorio Portilla

Observatorio Astronómico Nacional. Facultad de Ciencias. Universidad Nacional de Colombia. Apartado Aéreo 2584

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How to Cite

Portilla, J. G. (2023). THE RESTRICTED THREE BODY PROBLEM BY LIE SERIES. Revista De La Academia Colombiana De Ciencias Exactas, Físicas Y Naturales, 27(103), 165–172. https://doi.org/10.18257/raccefyn.27(103).2003.2059

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Abstract

Starting from the differential equations that describe the motion of a body of infinitesimal mass under the Newtonian gravitational field produced by two bodies of comparable mass which orbit in circular orbits about their common center of mass (circular, restricted, three-body problem), we obtained, by a Lie operator, solutions that permit, by recurrent algebraic expressions, to find the components of the position and velocity vectors by means of Lie series. We present a comparison between the numerical direct integrations and the solution by Lie series.

https://doi.org/10.18257/raccefyn.27(103).2003.2059

Keywords

Celestial Mechanics | Lie-series | Restricted three body problem

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