Abstract
The computer algebra methods are effective means for the search of approximate and exact solutions of differential equations of theoretical physics, celestial mechanics, astrodynamics, and other natural sciences. Before appearance of Programming Systems such as Mathematica, Maple etc., we knew for classical Newtonian three-body problem only Euler exact collinear and Lagrange triangular solutions, for many-body problem – the rotating regular tetragon solution found by A. Dziobek [1] and the general homographic solution theory developed by A. Winter [2] in the 30es of the 20th century. An amount of similar research [3,4,5,6,7,8,9,10] has grown recently due to the fact that the existence of central configurations of the many-body problem is eventually reduced to the solution of the systems of nonlinear algebraic-irrational equations, which can be solved only by the computer algebra methods, thanks to exceptional properties of them.
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Grebenicov, E.A., Kozak-Skoworodkin, D., Diarova, D.M. (2006). Numerical Study of Stability Domains of Hamiltonian Equation Solutions. In: Ganzha, V.G., Mayr, E.W., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2006. Lecture Notes in Computer Science, vol 4194. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11870814_15
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