Dynamical aspects of an equilateral restricted four-body problem
type: Item
instance of: scholarly article
title: Dynamical aspects of an equilateral restricted four-body problem
zbMATH Open document ID: 1184.70008
DOI: 10.1155/2009/181360
author: Claudio Vidal
author: Martha Alvarez-Ramírez
published in: Mathematical Problems in Engineering
publication date: 2010-04-23T00:00:00Z
full work available at URL: https://eudml.org/doc/229426
review text: Summary: The spatial equilateral restricted four-body problem (ERFBP) is a four body problem where a mass point of negligible mass is moving under the Newtonian gravitational attraction of three positive masses (called the primaries) which move on circular periodic orbits around their center of mass fixed at the origin of the coordinate system such that their configuration is always an equilateral triangle. Since fourth mass is small, it does not affect the motion of the three primaries. In our model we assume that the two masses of the primaries \(m_{2}\) and \(m_{3}\) are equal to \(\mu \) and the mass \(m_{1}\) is \(1 - 2\mu \). The Hamiltonian function that governs the motion of the fourth mass is derived and it has three degrees of freedom depending periodically on time. Using a synodical system, we fixed the primaries in order to eliminate the time dependence. Similarly to the circular restricted three-body problem, we obtain a first integral of motion. With the help of the Hamiltonian structure, we characterize the region of the possible motions and the surface of fixed level in the spatial as well as in the planar case. Among other things, we verify that the number of equilibrium solutions depends upon the masses, also we show the existence of periodic solutions by different methods in the planar case.
Mathematics Subject Classification ID: 70F10
Mathematics Subject Classification ID: 37N05
zbMATH DE Number: 5700432
Wikidata QID: Q58648899
MaRDI profile type: Publication
OpenAlex ID: W2061247127
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description: scientific article; zbMATH DE number 5700432