1,650 research outputs found
A New Approach for Analytical Computation of Hamiltonian of a Satellite Perturbed Motion
AbstractThe problem of computation of the Hamiltonian for the perturbed motion of an artificial Earth satellite with large eccentricity is considered. The method of calculation of items of the perturbing function, which is presented in the form of Jacobi nome series, is described. Some advantages of the new approach to the expansion of the Hamiltonian are shown by computations within computer algebra systems. Mathematical techniques for computations with elliptic functions, which are used in the suggested method of Hamiltonian expansion, are considered. Numerical verification and accuracy checking of analytical results is investigated by means of computer algebra system MAPLE
Short-axis-mode rotation of a free rigid body by perturbation series
A simple rearrangement of the torque free motion Hamiltonian shapes it as a
perturbation problem for bodies rotating close to the principal axis of maximum
inertia, independently of their triaxiality. The complete reduction of the main
part of this Hamiltonian via the Hamilton-Jacobi equation provides the
action-angle variables that ease the construction of a perturbation solution by
Lie transforms. The lowest orders of the transformation equations of the
perturbation solution are checked to agree with Kinoshita's corresponding
expansions for the exact solution of the free rigid body problem. For
approximately axisymmetric bodies rotating close to the principal axis of
maximum inertia, the common case of major solar system bodies, the new approach
is advantageous over classical expansions based on a small triaxiality
parameter.Comment: 22 pages, 1 figure, to be presented in 2013 AAS/AIAA Astrodynamics
Specialist Conference, Hilton Head, South Carolina, August 11 - 15, 201
HEOSAT: A mean elements orbit propagator program for Highly Elliptical Orbits
The algorithms used in the construction of a semi-analytical propagator for
the long-term propagation of Highly Elliptical Orbits (HEO) are described. The
software propagates mean elements and include the main gravitational and
non-gravitational effects that may affect common HEO orbits, as, for instance,
geostationary transfer orbits or Molniya orbits. Comparisons with numerical
integration show that it provides good results even in extreme orbital
configurations, as the case of SymbolX.Comment: 18 pages, 5 figure
A Hopf variables view on the libration points dynamics
The dynamics about the libration points of the Hill problem is investigated
analytically. In particular, the use of Lissajous variables and perturbation
theory allows to reduce the problem to a one degree of freedom Hamiltonian
depending on two physical parameters. The invariant manifolds structure of the
Hill problem is then disclosed, yet accurate computations are limited to energy
values close to that of the libration points
Element sets for high-order Poincar\'e mapping of perturbed Keplerian motion
The propagation and Poincar\'e mapping of perturbed Keplerian motion is a key
topic in celestial mechanics and astrodynamics, e.g. to study the stability of
orbits or design bounded relative trajectories. The high-order transfer map
(HOTM) method enables efficient mapping of perturbed Keplerian orbits over many
revolutions. For this, the method uses the high-order Taylor expansion of a
Poincar\'e or stroboscopic map, which is accurate close to the expansion point.
In this paper, we investigate the performance of the HOTM method using
different element sets for building the high-order map. The element sets
investigated are the classical orbital elements, modified equinoctial elements,
Hill variables, cylindrical coordinates and Deprit's ideal elements. The
performances of the different coordinate sets are tested by comparing the
accuracy and efficiency of mapping low-Earth and highly-elliptical orbits
perturbed by with numerical propagation. The accuracy of HOTM depends
strongly on the choice of elements and type of orbit. A new set of elements is
introduced that enables extremely accurate mapping of the state, even for high
eccentricities and higher-order zonal perturbations. Finally, the high-order
map is shown to be very useful for the determination and study of fixed points
and centre manifolds of Poincar\'e maps.Comment: Pre-print of journal articl
NIMASTEP: a software to modelize, study and analyze the dynamics of various small objects orbiting specific bodies
NIMASTEP is a dedicated numerical software developed by us, which allows one
to integrate the osculating motion (using cartesian coordinates) in a Newtonian
approach of an object considered as a point-mass orbiting a homogeneous central
body that rotates with a constant rate around its axis of smallest inertia. The
code can be applied to objects such as particles, artificial or natural
satellites or space debris. The central body can be either any terrestrial
planet of the solar system, any dwarf-planet, or even an asteroid. In addition,
very many perturbations can be taken into account, such as the combined
third-body attraction of the Sun, the Moon, or the planets, the direct solar
radiation pressure (with the central body shadow), the non-homogeneous
gravitational field caused by the non-sphericity of the central body, and even
some thrust forces. The simulations were performed using different integration
algorithms. Two additional tools were integrated in the software package; the
indicator of chaos MEGNO and the frequency analysis NAFF. NIMASTEP is designed
in a flexible modular style and allows one to (de)select very many options
without compromising the performance. It also allows one to easily add other
possibilities of use. The code has been validated through several tests such as
comparisons with numerical integrations made with other softwares or with
semi-analytical and analytical studies. The various possibilities of NIMASTEP
are described and explained and some tests of astrophysical interest are
presented. At present, the code is proprietary but it will be released for use
by the community in the near future. Information for contacting its authors and
(in the near future) for obtaining the software are available on the web site
http://www.fundp.ac.be/en/research/projects/page_view/10278201/Comment: Astronomy & Astrophysics - Received: 25 November 2011 / Accepted: 27
February 2012 -- 14 pages, 4 figure
Investigation of highly efficient satellite solution methods
Methods for analyzing the stability of satellites are discussed. The subjects considered are: (1) time elements, (2) stabilization by external energy corrections, and (3) long term global solutions for the synchronous satellite. A set of canonical two-body elements referred to as Delaunay-similar elements is presented. In contrast to the classical Delaunay theory which has time as the independent variable, the D-S theory uses an independent variable which is a generalized true anomaly. The numerical integration of the canonical perturbation equations of these elements is developed
Influence of the coorbital resonance on the rotation of the Trojan satellites of Saturn
The Cassini spacecraft collects high resolution images of the saturnian
satellites and reveals the surface of these new worlds. The shape and rotation
of the satellites can be determined from the Cassini Imaging Science Subsystem
data, employing limb coordinates and stereogrammetric control points. This is
the case for Epimetheus (Tiscareno et al. 2009) that opens elaboration of new
rotational models (Tiscareno et al. 2009; Noyelles 2010; Robutel et al. 2011).
Especially, Epimetheus is characterized by its horseshoe shape orbit and the
presence of the swap is essential to introduce explicitly into rotational
models. During its journey in the saturnian system, Cassini spacecraft
accumulates the observational data of the other satellites and it will be
possible to determine the rotational parameters of several of them. To prepare
these future observations, we built rotational models of the coorbital (also
called Trojan) satellites Telesto, Calypso, Helene, and Polydeuces, in addition
to Janus and Epimetheus. Indeed, Telesto and Calypso orbit around the L_4 and
L_5 Lagrange points of Saturn-Tethys while Helene and Polydeuces are coorbital
of Dione. The goal of this study is to understand how the departure from the
Keplerian motion induced by the perturbations of the coorbital body, influences
the rotation of these satellites. To this aim, we introduce explicitly the
perturbation in the rotational equations by using the formalism developed by
Erdi (1977) to represent the coorbital motions, and so we describe the
rotational motion of the coorbitals, Janus and Epimetheus included, in compact
form
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