The Mathematica book (4th edition)
The Mathematica book (4th edition)
Symbolic-numerical analysis of equilibrium solutions in a restricted four-body problem
Programming and Computing Software
On the stability of equilibrium positions in the circular restricted four-body problem
CASC'11 Proceedings of the 13th international conference on Computer algebra in scientific computing
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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.