Mathematics
Scientific paper
Jan 1985
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1985cemec..35...23f&link_type=abstract
Celestial Mechanics (ISSN 0008-8714), vol. 35, Jan. 1985, p. 23-43.
Mathematics
2
Celestial Bodies, Jacobi Integral, Liapunov Functions, Many Body Problem, Motion Stability, Virial Theorem, Branching (Mathematics), Cosmology, Einstein Equations, Electromagnetic Radiation, Pendulums, Schwarzschild Metric
Scientific paper
The Liapunov stability of the virial solutions of the n-body problem of celestial mechanics obtained by Ferronsky et al. (1978, 1979, 1981, and 1982) using Jacobi's (1884) equation, is investigated analytically, applying the permanent-perturbation criterion of Duboshin (1978). The Liapunov stability of the motion of a system described by coordinates and integral characteristics is examined; the stability of virial oscillations is determined; the equation of virial oscillations is derived directly from Einstein's equation for homogeneous isotropic space; the equivalence of the Schwarzschild solution and the solution of Jacobi's equation is demonstrated for the case of static description; and stability criteria for virial oscillations of celestial bodies emitting electromagnetic radiation are derived.
Denisik S. A.
Ferronskii S. V.
Ferronsky V. I.
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