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Ю.В. Баркин, М.Ю. Баркин
16
The movement of the solid core in the cavity
of a rotating non-spherical shell
© Yu.V. Barkin
1
,
M.Yu. Barkin
2
1
Sternberg Astronomical Institute at Lomonosov Moscow State University,
Moscow, 119991, Russia
2
Bauman Moscow State Technical University, Moscow, 105005, Russia
The article presents the analysis of the integrable cases of the restricted problem of
translational-rotational motion of a rigid body (core) in the cavity of steady rotating
gravitating non-spherical shell. Only the gravitational interaction of bodies is
considered. The canonical equations of rotational motion in Euler variables and Andoyer
variables were obtained
.
The cases of integrability of the restricted problem when the
core is an axisymmetric rigid body are studied.
In these cases solution of the problem is
reduced to a simple quadrature reversal and can be represented in terms of elliptic
functions.
This research reveals new possibilities for the study of relationships of core
and heavenly body mantle forced relative motions and variations of natural processes on
the planets and satellites.
Dynamic studies of the Earth mantle — liquid core — rigid
core system are of great interest for the modern geodynamics.
Keywords:
non-spherical rigid body, elliptic integrals, Andoyer variables, the mantle –
core system, microgravity, interaction of blocks, Space Station blocks.
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