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 SM ISO690:2012GREBENIKOV, Evgenii, PROKOPENYA, Alexandr. Studying stability of the equilibrium solutions in the restricted Newton’s problem of four bodies. In: Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2003, nr. 2(42), pp. 28-36. ISSN 1024-7696. |
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| Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica | ||||||
| Numărul 2(42) / 2003 / ISSN 1024-7696 /ISSNe 2587-4322 | ||||||
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| Pag. 28-36 | ||||||
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Newton’s restricted problem of four bodies is investigated. It has been
shown that there are six equilibrium solutions of the equations of motion. Stability
of these solutions is analyzed in linear approximation with computer algebra system
Mathematica. It has been proved that four radial solutions are unstable while two
bisector solutions are stable if the mass of the central body P0 is large enough. There
is also a domain of instability of the bisector solutions near the resonant point in the
space of parameters and its boundaries are found in linear approximation. |
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| Cuvinte-cheie Restricted problem of four bodies, equilibrium solutions, characteristic exponents., stability |
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