22 research outputs found
Nonlinear Stability in the Generalised Photogravitational Restricted Three Body Problem with Poynting-Robertson Drag
The Nonlinear stability of triangular equilibrium points has been discussed
in the generalised photogravitational restricted three body problem with
Poynting-Robertson drag. The problem is generalised in the sense that smaller
primary is supposed to be an oblate spheroid. The bigger primary is considered
as radiating. We have performed first and second order normalization of the
Hamiltonian of the problem. We have applied KAM theorem to examine the
condition of non-linear stability. We have found three critical mass ratios.
Finally we conclude that triangular points are stable in the nonlinear sense
except three critical mass ratios at which KAM theorem fails.Comment: Including Poynting-Robertson Drag the triangular equilibrium points
are stable in the nonlinear sense except three critical mass ratios at which
KAM theorem fail
The Effect of Radiation Pressure on the Equilibrium Points in the Generalised Photogravitational Restricted Three Body Problem
The existence of equilibrium points and the effect of radiation pressure have
been discussed numerically. The problem is generalized by considering bigger
primary as a source of radiation and small primary as an oblate spheroid. We
have also discussed the Poynting-Robertson(P-R) effect which is caused due to
radiation pressure. It is found that the collinear points deviate
from the axis joining the two primaries, while the triangular points
are not symmetrical due to radiation pressure. We have seen that
are linearly unstable while are conditionally stable in the sense of
Lyapunov when P-R effect is not considered. We have found that the effect of
radiation pressure reduces the linear stability zones while P-R effect induces
an instability in the sense of Lyapunov
Influence of fast interstellar gas flow on dynamics of dust grains
The orbital evolution of a dust particle under the action of a fast
interstellar gas flow is investigated. The secular time derivatives of
Keplerian orbital elements and the radial, transversal, and normal components
of the gas flow velocity vector at the pericentre of the particle's orbit are
derived. The secular time derivatives of the semi-major axis, eccentricity, and
of the radial, transversal, and normal components of the gas flow velocity
vector at the pericentre of the particle's orbit constitute a system of
equations that determines the evolution of the particle's orbit in space with
respect to the gas flow velocity vector. This system of differential equations
can be easily solved analytically. From the solution of the system we found the
evolution of the Keplerian orbital elements in the special case when the
orbital elements are determined with respect to a plane perpendicular to the
gas flow velocity vector. Transformation of the Keplerian orbital elements
determined for this special case into orbital elements determined with respect
to an arbitrary oriented plane is presented. The orbital elements of the dust
particle change periodically with a constant oscillation period or remain
constant. Planar, perpendicular and stationary solutions are discussed.
The applicability of this solution in the Solar system is also investigated.
We consider icy particles with radii from 1 to 10 micrometers. The presented
solution is valid for these particles in orbits with semi-major axes from 200
to 3000 AU and eccentricities smaller than 0.8, approximately. The oscillation
periods for these orbits range from 10^5 to 2 x 10^6 years, approximately.Comment: 22 pages, 3 figures; Accepted for publication in Celestial Mechanics
and Dynamical Astronom