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Symbolic–Numerical Methods for Searching Equilibrium States in a Restricted FourBody Problem

D. A. Budzkoa
A. N. Prokopenyab
Journal / Anthology

Programming and Computer Software
Year: 2013
Volume: 39
Issue: 2
Page range: 74–80

Algorithms for searching equilibrium solutions of the circular restricted fourbody problem for mulated on the basis of the triangular Lagrange solutions of the threebody problem are discussed. An algo rithm 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 equilib rium 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.