Symbolic-numerical methods for searching equilibrium states in a restricted four-body problem

Algorithms for searching equilibrium solutions of the circular restricted four-body problem formulated on the basis of the triangular Lagrange solutions of the three-body problem are discussed. An algorithm is proposed for calculating the bifurcation curve in the plane of system parameters that sepa...

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Bibliographic Details
Published in:Programming and computer software Vol. 39; no. 2; pp. 74 - 80
Main Authors: Budzko, D. A., Prokopenya, A. N.
Format: Journal Article
Language:English
Published: Dordrecht SP MAIK Nauka/Interperiodica 01.03.2013
Springer Nature B.V
Subjects:
Algorithms
Artificial Intelligence
Bifurcations
Computer algebra
Computer programs
Computer Science
Equilibrium methods
Four body problem
Mathematical analysis
Mathematical models
Numerical methods
Operating Systems
Parameters
Power series
Programming
Search algorithms
Searching
Software
Software Engineering
Software Engineering/Programming and Operating Systems
Three body problem
Body Problem
Equilibrium Position
Equilibrium Solution
Bifurcation Point
Libration Point
ISSN:0361-7688, 1608-3261
Online Access:Get full text
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Summary:Algorithms for searching equilibrium solutions of the circular restricted four-body problem formulated on the basis of the triangular Lagrange solutions of the three-body problem are discussed. An algorithm is proposed for calculating the bifurcation curve in the plane of system parameters that separates domains of the eight and ten equilibrium solutions. For the parameter values corresponding to the bifurcation curve, the system has nine equilibrium solutions. In the neighborhood of the bifurcation points, the equilibrium solutions are found in the form of power series in terms of a small parameter. The dependence of these solutions on the system parameters is studied numerically. Codes of algorithms implemented in the computer algebra system Mathematica are presented.
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ISSN:0361-7688
1608-3261
DOI:10.1134/S0361768813020035