9 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
Mission design through averaging of perturbed Keplerian systems: the paradigm of an Enceladus orbiter
Symplectic coordinates on S2 × S2 for perturbed Keplerian problems: Application to the dynamics of a generalised Størmer problem
In order to analyse the dynamics of a given Hamiltonian system in the space defined as the Cartesian product of two spheres, we propose to combine Delaunay coordinates with Poincaré-like coordinates. The coordinates are of local character and have to be selected accordingly with the type of motions one has to take into consideration, so we distinguish the following types: (i) rectilinear motions; (ii) circular and equatorial motions; (iii) circular non-equatorial motions; (iv) non-circular equatorial motions; and (v) non-circular and non-equatorial motions. We apply the theory to study the dynamics of the reduced flow of a generalised Størmer problem that is modelled as a perturbation of the Kepler problem. After using averaging and reduction theories, the corresponding flow is analysed on the manifold S2×S2, calculating the occurring equilibria and their stability. Finally, the flow of the original problem is reconstructed, concluding the existence of some families of periodic solutions and KAM tori. © 2010 Elsevier Inc
The Keplerian regime of charged particles in planetary magnetospheres
The dynamics of a charged particle orbiting around a rotating magnetic planet is studied. The system is modelled by the two-body Hamiltonian perturbed by an axially-symmetric function which goes to infinity as soon as the particle approaches the planet. The perturbation consists in a magnetic dipole field and a corotational electric field. When it is weak compared to the Keplerian part of the Hamiltonian, we average the system with respect to the mean anomaly up to first order in terms of a small parameter defined by the ratio between the magnetic and the Keplerian interactions. After dropping higher-order terms, we use invariant theory to reduce the averaged system by virtue of its continuous and discrete symmetries, determining also the successive reduced phase spaces. Then, we study the flow of the resulting system in the most reduced phase space, describing all equilibria and their stability, as well as the different classes of bifurcations. Finally, we connect the analysis of the flow on these reduced phase spaces with the one of the original system. © 2004 Published by Elsevier B.V
Periodic Solutions of the Elliptic Isosceles Restricted Three-Body Problem with Collision by the Averaging Method
FRIPON: a worldwide network to track incoming meteoroids
Context: Until recently, camera networks designed for monitoring fireballs worldwide were not fully automated, implying that in case of a meteorite fall, the recovery campaign was rarely immediate. This was an important limiting factor as the most fragile – hence precious – meteorites must be recovered rapidly to avoid their alteration.
Aims: The Fireball Recovery and InterPlanetary Observation Network (FRIPON) scientific project was designed to overcome this limitation. This network comprises a fully automated camera and radio network deployed over a significant fraction of western Europe and a small fraction of Canada. As of today, it consists of 150 cameras and 25 European radio receivers and covers an area of about 1.5 × 106 km2.
Methods: The FRIPON network, fully operational since 2018, has been monitoring meteoroid entries since 2016, thereby allowing the characterization of their dynamical and physical properties. In addition, the level of automation of the network makes it possible to trigger a meteorite recovery campaign only a few hours after it reaches the surface of the Earth. Recovery campaigns are only organized for meteorites with final masses estimated of at least 500 g, which is about one event per year in France. No recovery campaign is organized in the case of smaller final masses on the order of 50 to 100 g, which happens about three times a year; instead, the information is delivered to the local media so that it can reach the inhabitants living in the vicinity of the fall.
Results: Nearly 4000 meteoroids have been detected so far and characterized by FRIPON. The distribution of their orbits appears to be bimodal, with a cometary population and a main belt population. Sporadic meteors amount to about 55% of all meteors. A first estimate of the absolute meteoroid flux (mag < –5; meteoroid size ≥~1 cm) amounts to 1250/yr/106 km2. This value is compatible with previous estimates. Finally, the first meteorite was recovered in Italy (Cavezzo, January 2020) thanks to the PRISMA network, a component of the FRIPON science project