Stability of the Stationary Solutions of the Differential Equations of Restricted Newtonian Problem with Incomplete Symmetry
نویسنده
چکیده
We investigate the Lyapunov stability of the stationary solutions of the differential equations of restricted six-body problem with the gravitational centre. The gravitational field is created by bodies P0, P1, P2, P3 and P4 with masses m0, m1, m2, m3 and m4, respectively. In this gravitational field the movement of a body P with zero mass (m = 0) is investigated. The bodies P1, P2, P3 and P4 form a rhombus, rotating uniformly around the centre of gravity P0. In the article we have formulated necessary and sufficient conditions of Lyapunov stability and instability of equilibrium point of this model. All necessary analytical calculations are executed in the system of symbolical calculations (SSC) “Mathematica”.
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