128 research outputs found
Modern Problems of Celestial Mechanics
Survey on celestial mechanics problem
Cartesian approach for constrained mechanical system with three degree of freedom
In the history of mechanics, there have been two points of view for studying
mechanical systems: The Newtonian and the Cartesian.
According the Descartes point of view, the motion of mechanical systems is
described by the first-order differential equations in the dimensional
configuration space \textsc{Q}.
In this paper we develop the Cartesian approach for mechanical systems with
three degrees of freedom and with constraint which are linear with respect to
velocity. The obtained results we apply to discuss the integrability of the
geodesic flows on the surface in the three dimensional Euclidian space and to
analyze the integrability of a heavy rigid body in the Suslov and the Veselov
cases
Relative equilibria in the unrestricted problem of a sphere and symmetric rigid body
We consider the unrestricted problem of two mutually attracting rigid bodies,
an uniform sphere (or a point mass) and an axially symmetric body. We present a
global, geometric approach for finding all relative equilibria (stationary
solutions) in this model, which was already studied by Kinoshita (1970). We
extend and generalize his results, showing that the equilibria solutions may be
found by solving at most two non-linear, algebraic equations, assuming that the
potential function of the symmetric rigid body is known explicitly. We
demonstrate that there are three classes of the relative equilibria, which we
call "cylindrical", "inclined co-planar", and "conic" precessions,
respectively. Moreover, we also show that in the case of conic precession,
although the relative orbit is circular, the point-mass and the mass center of
the body move in different parallel planes. This solution has been yet not
known in the literature.Comment: The manuscript with 10 pages, 5 figures; accepted to the Monthly
Notices of the Royal Astronomical Societ
Elliptical motions of stars in close binary systems
Motions of stars in close binary systems with a conservative mass exchange
are examined. It is shown that Paczynski-Huang model widely used now for
obtaining the semi-major axis variation of a relative stars orbit is incorrect,
because it brings about large mistakes. A new model suitable for elliptical
orbits of stars is proposed. Both of reactive and attractive forces between
stars and a substance of the flowing jet are taken into account. A possibility
of a mass exchange at presence of accretion disk is considere
Spectrometric method to detect exoplanets as another test to verify the invariance of the velocity of light
Hypothetical influences of variability of light velocity due to the
parameters of the source of radiation, for the results of spectral measurements
of stars to search for exoplanets are considered. Accounting accelerations of
stars relative to the barycenter of the star - a planet (the planets) was
carried out. The dependence of the velocity of light from the barycentric
radial velocity and barycentric radial acceleration component of the star
should lead to a substantial increase (up to degree of magnitude) semi-major
axes of orbits detected candidate to extrasolar planets. Consequently, the
correct comparison of the results of spectral method with results of other
well-known modern methods of detecting extrasolar planets can regard the
results obtained in this paper as a reliable test for testing the invariance of
the velocity of light.Comment: 11 pages, 5 figure
- …