Dynamical Aspects of an Equilateral Restricted Four-Body Problem
Joint Authors
Álvarez-Ramírez, Martha
Vidal, Claudio
Source
Mathematical Problems in Engineering
Issue
Vol. 2009, Issue 2009 (31 Dec. 2009), pp.1-23, 23 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2010-03-03
Country of Publication
Egypt
No. of Pages
23
Main Subjects
Abstract EN
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 m2 and m3 are equal to μ and the mass m1 is 1−2μ.
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.
American Psychological Association (APA)
Álvarez-Ramírez, Martha& Vidal, Claudio. 2010. Dynamical Aspects of an Equilateral Restricted Four-Body Problem. Mathematical Problems in Engineering،Vol. 2009, no. 2009, pp.1-23.
https://search.emarefa.net/detail/BIM-452416
Modern Language Association (MLA)
Álvarez-Ramírez, Martha& Vidal, Claudio. Dynamical Aspects of an Equilateral Restricted Four-Body Problem. Mathematical Problems in Engineering No. 2009 (2009), pp.1-23.
https://search.emarefa.net/detail/BIM-452416
American Medical Association (AMA)
Álvarez-Ramírez, Martha& Vidal, Claudio. Dynamical Aspects of an Equilateral Restricted Four-Body Problem. Mathematical Problems in Engineering. 2010. Vol. 2009, no. 2009, pp.1-23.
https://search.emarefa.net/detail/BIM-452416
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-452416