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1.
Mass-weighted symplectic forms provide a unified framework for the treatment of both finite and vanishingly small masses in
the N-body problem. These forms are introduced, compared to previous approaches, and their properties are discussed. Applications
to symplectic mappings, the definition of action-angle variables for the Kepler problem, and Hamiltonian perturbation theory
are outlined
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
2.
Liam M. Healy 《Celestial Mechanics and Dynamical Astronomy》2003,85(2):175-207
The Lie transfer map method may be applied to orbit propagation problems in celestial mechanics. This method, described in another paper, is a perturbation method applicable to Hamiltonian systems. In this paper, it is used to calculate orbits for zonal perturbations to the Kepler (two-body) problem, in both expansion in the eccentricity and closed form. In contrast with a normal form method like that of Deprit, the Lie transformations here are used to effect a propagation of phase space in time, and not to transform one Hamiltonian into another. 相似文献
3.
Bruno Cordani 《Celestial Mechanics and Dynamical Astronomy》2004,89(2):165-179
A method for the expansion of the perturbative Hamiltonian in the planetary problem is presented, which allows one to immediately
detect the terms vanishing under the averaging process. The method bases itself on a geometrical analysis, through the groups
SO(3) and SU(2), of the Poincaré canonical variables or of the similar Laplace variables. As an outcome, one obtains a MAPLE
program, which calculates the first averaged terms of the perturbative Hamiltonian.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
4.
Liam M. Healy 《Celestial Mechanics and Dynamical Astronomy》2000,76(2):79-120
Using the elimination of the parallax followed by the Delaunay normalization, we present a procedure for calculating a normal
form of the main problem (J
2 perturbation only) in satellite theory. This procedure is outlined in such a way that an object-oriented automatic symbolic
manipulator based on a hierarchy of algebras can perform this computation. The Hamiltonian after the Delaunay normalization
is presented to order six explicitly in closed form, that is, in which there is no expansion in the eccentricity. The corresponding
generating function and transformation of coordinates, too lengthy to present here to the same order; the generator is given
through order four.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
5.
The Sitnikov problem is one of the most simple cases of the elliptic restricted three body system. A massless body oscillates
along a line (z) perpendicular to a plane (x,y) in which two equally massive bodies, called primary masses, perform Keplerian orbits around their common barycentre with
a given eccentricity e. The crossing point of the line of motion of the third mass with the plane is equal to the centre of gravity of the entire
system. In spite of its simple geometrical structure, the system is nonlinear and explicitly time dependent. It is globally
non integrable and therefore represents an interesting application for advanced perturbative methods. In the present work
a high order perturbation approach to the problem was performed, by using symbolic algorithms written in Mathematica. Floquet
theory was used to derive solutions of the linearized equation up to 17th order in e. In this way precise analytical expressions for the stability of the system were obtained. Then, applying the Courant and
Snyder transformation to the nonlinear equation, algebraic solutions of seventh order in z and e were derived using the method of Poincaré–Lindstedt. The enormous amount of necessary computations were performed by extensive
use of symbolic programming. We developed automated and highly modularized algorithms in order to master the problem of ordering
an increasing number of algebraic terms originating from high order perturbation theory. 相似文献
6.
We consider the non-canonical Hamiltonian dynamics of a gyrostat in Newtonian interaction with n spherical rigid bodies. Using the symmetries of the system we carry out two reductions. Then, working in the reduced problem,
we obtain the equations of motion, a Casimir function of the system and the equations that determine the relative equilibria.
Global conditions for existence of relative equilibria are given. Besides, we give the variational characterization of these
equilibria and three invariant manifolds of the problem; being calculated the equations of motion in these manifolds, which
are described by means of a canonical Hamiltonian system. We give some Eulerian and Lagrangian equilibria for the four body
problem with a gyrostat. Finally, certain classical problems of Celestial Mechanics are generalized. 相似文献
7.
The problem of three bodies when one of them is a gyrostat is considered. Using the symmetries of the system we carry out two reductions. Global considerations about the conditions for relative equilibria are made. Finally, we restrict to an approximated model of the dynamics and a complete study of the relative equilibria is made. 相似文献
8.
The recent numerical simulations of Tittemore and Wisdom (1988, 1989, 1990) and Dermottet al. (1988), Malhotra and Dermott (1990) concerning the tidal evolution through resonances of some pairs of Uranian satellites have revealed interesting dynamical phenomena related to the interactions between close-by resonances. These interactions produce chaotic layers and strong secondary resonances. The slow evolution of the satellite orbits in this dynamical landscape is responsible for temporary capture into resonance, enhancement of eccentricity or inclination and subsequent escape from resonance. The present contribution aims at developing analytical tools for predicting the location and size of chaotic layers and secondary resonances. The problem of the 3:1 inclination resonance between Miranda and Umbriel is analysed. 相似文献