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Численно-аналитическое построение семейства периодических движений…
Инженерный журнал: наука и инновации
# 5·2016 9
Numerical analysis of periodic motions of a dynamically
symmetric satellite originated from its hyperboloidal
precession
© E.A. Sukhov, B.S.Bardin
Moscow Aviation Institute (MAI), Moscow, 125993, Russia
The article presents families of periodic satellite movements originated from its hyperbo-
loidal precession as a special case of a dynamically symmetric satellite — solid body
motion about the center of mass in a circular orbit
.
The parameters of the family are total
mechanical energy deviation from its value on the hyperboloidal precession and the ratio
of the polar and equatorial moments of inertia of the satellite (inertial parameter).When
energy values are close to the value in the hyperboloidal precession, periodic motions
are obtained by Lyapunov technique as convergent series. For arbitrary values of energy
for obtaining periodic motions numerical parameter continuation method for solution
families proposed by A.G. Sokolskiy and S.R. Karimov was applied. The research tech-
niques are described briefly, recommendations on the selecting the parameter increments
are set out, the results of constructing a family of periodic motions originated from satel-
lite hyperboloidal precession are presented.
Keywords:
hamiltonian mechanics, numerical methods, periodic motions, symmetric sat-
ellite, hyperboloidal precession.
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