26 research outputs found
Equilibria, periodic orbits around equilibria, and heteroclinic connections in the gravity field of a rotating homogeneous cube
This paper investigates the dynamics of a particle orbiting around a rotating
homogeneous cube, and shows fruitful results that have implications for
examining the dynamics of orbits around non-spherical celestial bodies. This
study can be considered as an extension of previous research work on the
dynamics of orbits around simple shaped bodies, including a straight segment, a
circular ring, an annulus disk, and simple planar plates with backgrounds in
celestial mechanics. In the synodic reference frame, the model of a rotating
cube is established, the equilibria are calculated, and their linear
stabilities are determined. Periodic orbits around the equilibria are computed
using the traditional differential correction method, and their stabilities are
determined by the eigenvalues of the monodromy matrix. The existence of
homoclinic and heteroclinic orbits connecting periodic orbits around the
equilibria is examined and proved numerically in order to understand the global
orbit structure of the system. This study contributes to the investigation of
irregular shaped celestial bodies that can be divided into a set of cubes.Comment: 29 pages, 16 figures, accepted for publication in Astrophysics &
Space Scienc
Periodic orbits in the gravity field of a fixed homogeneous cube
In the current study, the existence of periodic orbits around a fixed
homogeneous cube is investigated, and the results have powerful implications
for examining periodic orbits around non-spherical celestial bodies. In the two
different types of symmetry planes of the fixed cube, periodic orbits are
obtained using the method of the Poincar\'e surface of section. While in
general positions, periodic orbits are found by the homotopy method. The
results show that periodic orbits exist extensively in symmetry planes of the
fixed cube, and also exist near asymmetry planes that contain the regular Hex
cross section. The stability of these periodic orbits is determined on the
basis of the eigenvalues of the monodromy matrix. This paper proves that the
homotopy method is effective to find periodic orbits in the gravity field of
the cube, which provides a new thought of searching for periodic orbits around
non-spherical celestial bodies. The investigation of orbits around the cube
could be considered as the first step of the complicated cases, and helps to
understand the dynamics of orbits around bodies with complicated shapes. The
work is an extension of the previous research work about the dynamics of orbits
around some simple shaped bodies, including a straight segment, a circular
ring, an annulus disk, and simple planar plates.Comment: 23 pages, 10 figures, accepted for publication in Astrophysics &
Space Scienc
Long-term perturbations due to a disturbing body in elliptic inclined orbit
In the current study, a double-averaged analytical model including the action
of the perturbing body's inclination is developed to study third-body
perturbations. The disturbing function is expanded in the form of Legendre
polynomials truncated up to the second-order term, and then is averaged over
the periods of the spacecraft and the perturbing body. The efficiency of the
double-averaged algorithm is verified with the full elliptic restricted
three-body model. Comparisons with the previous study for a lunar satellite
perturbed by Earth are presented to measure the effect of the perturbing body's
inclination, and illustrate that the lunar obliquity with the value 6.68\degree
is important for the mean motion of a lunar satellite. The application to the
Mars-Sun system is shown to prove the validity of the double-averaged model. It
can be seen that the algorithm is effective to predict the long-term behavior
of a high-altitude Martian spacecraft perturbed by Sun. The double-averaged
model presented in this paper is also applicable to other celestial systems.Comment: 28 pages, 6 figure
On the a and g families of symmetric periodic orbits in the photo-gravitational hill problem and their application to asteroids
This paper focuses on the exploration of families of planar symmetric periodic orbits around minor bodies under the effect of solar radiation pressure. For very small asteroids and comets, an extension of the Hill problem with Solar Radiation Pressure (SRP) perturbation is a particularly well-suited dynamical model. The evolution of the a and g families of symmetric periodic orbits has been studied in this model when SRP is increased from the classical problem with no SRP to levels corresponding to current and future planned missions to minor bodies, as well as one extreme case with very large SRP. In addition, the feasibility an applicability of these orbits for the case of asteroids was analysed, and the effect of SRP in their stability is presented
Factor V leiden mutation, prothrombin gene mutation, and deficiences in coagulation inhibitors associated with budd-chiari syndrome and portal vein thrombosis: results of a case-control study.
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