共查询到20条相似文献，搜索用时 93 毫秒
1.
Osman M. Kamel 《Earth, Moon, and Planets》1993,62(2):131-138
Motivated by the recent proposals of A. Abian, we introduce the physical and dynamical considerations for producing a second Earth-like planet on which life sustaining conditions may exist, and hence we acquire multiplication of the cosmic resources of the human race. We investigate the perturbations in our solar system after alteration, through a third order Hamiltonian planetary theory for the eight principal planets. The Hori-Lie theorem, the Jacobi-Radau coordinates, and the canonical variables of H. Poincaré are adopted. 相似文献
2.
Jared M. Maruskin 《Celestial Mechanics and Dynamical Astronomy》2010,108(3):265-274
In this paper we derive an explicit, analytic formula for the geodesic distance between two points in the space of bounded
Keplerian orbits in a particular topology. The specific topology we use is that of a cone passing through the direct product
of two spheres. The two spheres constitute the configuration manifold for the space of bounded orbits of constant energy.
We scale these spheres by a factor equal to the semi-major axis of the orbit, forming a linear cone. This five-dimensional
manifold inherits a Riemannian metric, which is induced from the Euclidean metric on
\mathbbR6{\mathbb{R}^6}, the space in which it is embedded. We derive an explicit formula for the geodesic distance between any two points in this
space, each point representing a physical, gravitationally bound Keplerian orbit. Finally we derive an expression for the
Riemannian metric that we used in terms of classical orbital elements, which may be thought of as local coordinates on our
configuration manifold. 相似文献
3.
We derive a Hamiltonian which describes the first-order perturbations of orbital eccentricity and apse precession rate of a narrow ring due to a close satellite whose orbit is also eccentric. Our treatment covers cases in which the satellite crosses the ring. The level curves of the Hamiltonian are displayed for several values of the parameters. We apply our results to the interaction of Saturn's F ring with its inner shepherd satellite. 相似文献
4.
The Unified State Model is a method for expressing orbits using a set of seven elements. The elements consist of a quaternion
and three parameters based on the velocity hodograph. A complete derivation of the original model is given in addition to
two proposed modifications. Both modifications reduce the number of state elements from seven to six by replacing the quaternion
with either modified Rodrigues parameters or the Exponential Map. Numerical simulations comparing the original Unified State
Model, the Unified State Model with modified Rodrigues parameters, and the Unified State Model with Exponential Map, with
the traditional Cartesian coordinates have been carried out. The Unified State Model and its derivatives outperform the Cartesian
coordinates for all orbit cases in terms of accuracy and computational speed, except for highly eccentric perturbed orbits.
The performance of the Unified State Model is exceptionally better for the case of orbits with continuous low-thrust propulsion
with CPU simulation time being an order of magnitude lower than for the simulation using Cartesian coordinates. This makes
the Unified State Model an excellent state propagator for mission optimizations. 相似文献
5.
We derive the classical Delaunay variables by finding a suitable symmetry action of the three torus T3 on the phase space of the Kepler problem, computing its associated momentum map and using the geometry associated with this structure. A central feature in this derivation is the identification of the mean anomaly as the angle variable for a symplectic S
1 action on the union of the non-degenerate elliptic Kepler orbits. This approach is geometrically more natural than traditional ones such as directly solving Hamilton–Jacobi equations, or employing the Lagrange bracket. As an application of the new derivation, we give a singularity free treatment of the averaged J
2-dynamics (the effect of the bulge of the Earth) in the Cartesian coordinates by making use of the fact that the averaged J
2-Hamiltonian is a collective Hamiltonian of the T3 momentum map. We also use this geometric structure to identify the drifts in satellite orbits due to the J
2 effect as geometric phases. 相似文献
6.
Alessandra Celletti Fabrizio Paita Giuseppe Pucacco 《Celestial Mechanics and Dynamical Astronomy》2018,130(2):15
We study the dynamics of the de Sitter resonance, namely the stable equilibrium configuration of the first three Galilean satellites. We clarify the relation between this family of configurations and the more general Laplace resonant states. In order to describe the dynamics around the de Sitter stable equilibrium, a one-degree-of-freedom Hamiltonian normal form is constructed and exploited to identify initial conditions leading to the two families. The normal form Hamiltonian is used to check the accuracy in the location of the equilibrium positions. Besides, it gives a measure of how sensitive it is with respect to the different perturbations acting on the system. By looking at the phase plane of the normal form, we can identify a Laplace-like configuration, which highlights many substantial aspects of the observed one. 相似文献
7.
N. R. Sibgatullin 《Astronomy Letters》2002,28(2):83-88
We derive a formula for the nodal precession frequency and the Keplerian period of a particle at an arbitrary orbital inclination (with a minimum latitudinal angle reached at the orbit) in the post-Newtonian approximation in the external field of an oblate rotating neutron star (NS). We also derive formulas for the nodal precession and periastron rotation frequencies of slightly inclined low-eccentricity orbits in the field of a rapidly rotating NS in the form of asymptotic expansions whose first terms are given by the Okazaki-Kato formulas. The NS gravitational field is described by the exact solution of the Einstein equation that includes the NS quadrupole moment induced by rapid rotation. Convenient asymptotic formulas are given for the metric coefficients of the corresponding space-time in the form of Kerr metric perturbations in Boyer-Lindquist coordinates. 相似文献
8.
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
9.
We have performed normalization of Hamiltonian in the generalized photogravitational restricted three body problem with Poynting–Robertson
drag. In this problem we have taken bigger primary as source of radiation and smaller primary as an oblate spheroid. Whittaker’s
method is used to transform the second order part of the Hamiltonian into the normal form.
相似文献
10.
We propose the Ptolemaic transformation: a canonical change of variables reducing the Keplerian motion to the form of a perturbed Hamiltonian problem. As a solution of the unperturbed case, the Ptolemaic variables define an intermediary orbit, accurate up to the first power of eccentricity, like in the kinematic model of Claudius Ptolemy. In order to normalize the perturbed Hamiltonian we modify the recurrent Lie series algorithm of HoriuuMersman. The modified algorithm accounts for the loss of a term's order during the evaluation of a Poisson bracket, and thus can be also applied in resonance problems. The normalized Hamiltonian consists of a single Keplerian term; the mean Ptolemaic variables occur to be trivial, linear functions of the Delaunay actions and angles. The generator of the transformation may serve to expand various functions in Poisson series of eccentricity and mean anomaly. 相似文献
11.
J. M. Ferrándiz 《Celestial Mechanics and Dynamical Astronomy》1987,41(1-4):343-357
In this paper, we present a canonical transformation that extends the change of coordinates of Cartesian type into the associate homogeneous coordinates, and provides a redundant set of eight canonical variables to describe the orbital motion of a particle. The transformed problem has two additional integrals, since the transformation increases the number of variables. Using these variables and a time proportional to the true anomaly, the Kepler problem can be reduced to a 4-dimensional oscillator, whose frequency can be selected to be either the magnitude of the angular momentum or unity, depending on a suitable scaling.Perturbed problems are represented by perturbed harmonic oscillators, whatever the type of the orbit is, and in the special case of central force fields, the resulting equations can be linearized exactly. 相似文献
12.
This paper presents a Hamiltonian approach to modelling spacecraft motion relative to a circular reference orbit based on
a derivation of canonical coordinates for the relative state-space dynamics. The Hamiltonian formulation facilitates the modelling
of high-order terms and orbital perturbations within the context of the Clohessy–Wiltshire solution. First, the Hamiltonian
is partitioned into a linear term and a high-order term. The Hamilton–Jacobi equations are solved for the linear part by separation,
and new constants for the relative motions are obtained, called epicyclic elements. The influence of higher order terms and
perturbations, such as Earth’s oblateness, are incorporated into the analysis by a variation of parameters procedure. As an
example, closed-form solutions for J2-invariant orbits are obtained. 相似文献
13.
Osman M. Kamel 《Earth, Moon, and Planets》1992,59(2):111-140
We eliminate the 1:2 critical terms — after a previous elimination of the short period terms — in the Hamiltonian of a first order U-N theory. We take into account terms of degree 0, 1, 2, 3, 4 in the eccentricity-inclination. We apply for this elimination the Hori-Lie technique through the Poincaré canonical variables and the Jacobi coordinates. The purely principal first order secular U-N Hamiltonian admits a complete solution. We obtained the U-N equations of motion generated by the principal first order long period U-N Hamiltonian which will be solved later. This part III is closely related to the two previous papers (Kamel, 1982, 1983). 相似文献
14.
Deprit and Miller have conjectured that normalization of integrable Hamiltonians may produce normal forms exhibiting degenerate equilibria to very high order. Several examples in the class of coupled elliptic oscillators are known. In order to test the utility of normalization as a detector of integrability we normalize, to high order, a perturbed Keplerian system known to have several integrable limits; the generalized van der Waals Hamiltonian for a hydrogen atom. While the separable limits give rise to high order degeneracy we find a non-separable, integrable limit for which the normal form does not exhibit degeneracy. We conclude that normalization may, in certain cases, indicate integrability but is not guaranteed to uncover all integrable limits. 相似文献
15.
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
16.
Osman M. Kamel 《Earth, Moon, and Planets》1992,57(1):23-64
In this paper we eliminate in a first order U-N theory the 1 : 2 critical terms up to the third degree with respect to eccentricity — inclination in both parts, main and indirect of the U-N planetary Hamiltonian. We operate the Von Zeipel technique. We adopt, in this theory, the Jacobi-Radau coordinates, and the Poincaré canonical variables. We neglect powers higher than the third in the eccentricity-inclination. This paper is related to the two previous articles (Kamel, 1982; 1983). 相似文献
17.
The regularization of a new problem, namely the three-body problem, using ‘similar’ coordinate system is proposed. For this
purpose we use the relation of ‘similarity’, which has been introduced as an equivalence relation in a previous paper (see
Roman in Astrophys. Space Sci. doi:, 2011). First we write the Hamiltonian function, the equations of motion in canonical form, and then using a generating function,
we obtain the transformed equations of motion. After the coordinates transformations, we introduce the fictitious time, to
regularize the equations of motion. Explicit formulas are given for the regularization in the coordinate systems centered
in the more massive and the less massive star of the binary system. The ‘similar’ polar angle’s definition is introduced,
in order to analyze the regularization’s geometrical transformation. The effect of Levi-Civita’s transformation is described
in a geometrical manner. Using the resulted regularized equations, we analyze and compare these canonical equations numerically,
for the Earth-Moon binary system. 相似文献
18.
The D'Alembert model for the spin/orbit problem in celestial mechanics is considered. Using a Hamiltonian formalism, it is shown that in a small neighborhood of a p:q spin/orbit resonance with (p,q) different from (1,1) and (2,1) the 'effective' D'Alembert Hamiltonian is a completely integrable system with phase space foliated by maximal invariant curves; instead, in a small neighborhood of a p:q spin/orbit resonance with (p,q) equal to (1,1) or (2,1) the 'effective' D'Alembert Hamiltonian has a phase portrait similar to that of the standard pendulum (elliptic and hyperbolic equilibria, separatrices, invariant curves of different homotopy). A fast averaging with respect to the 'mean anomaly' is also performed (by means of Nekhoroshev techniques) showing that, up to exponentially small terms, the resonant D'Alembert Hamiltonian is described by a two-degrees-of-freedom, properly degenerate Hamiltonian having the lowest order terms corresponding to the 'effective' Hamiltonian mentioned above. 相似文献
19.
Relative magnetic helicity, as a conserved quantity of ideal magnetohydrodynamics, has been highlighted as an important quantity
to study in plasma physics. Due to its nonlocal nature, its estimation is not straightforward in both observational and numerical
data. In this study we derive expressions for the practical computation of the gauge-independent relative magnetic helicity
in three-dimensional finite domains. The derived expressions are easy to implement and rapid to compute. They are derived
in Cartesian coordinates, but can be easily written in other coordinate systems. We apply our method to a numerical model
of a force-free equilibrium containing a flux rope, and compare the results with those obtained employing known half-space
equations. We find that our method requires a much smaller volume than half-space expressions to derive the full helicity
content. We also prove that values of relative magnetic helicity of different magnetic fields can be compared with each other
in the same sense as free-energy values can. Therefore, relative magnetic helicity can be meaningfully and directly compared
between different datasets, such as those from different active regions, but also within the same dataset at different times.
Typical applications of our formulae include the helicity computation in three-dimensional models of the solar atmosphere,
e.g., coronal-field reconstructions by force-free extrapolation and discretized magnetic fields of numerical simulations. 相似文献
20.
We studied the stability of the restricted circular three-body problem. We introduced a model Hamiltonian in action-angle Delaunay variables. which is nearly-integrable with the perturbing parameter representing the mass ratio of the primaries. We performed a normal form reduction to remove the perturbation in the initial Hamiltonian to higher orders in the perturbing parameter. Next we applied a result on the Nekhoroshev theorem proved by Pöschel [13] to obtain the confinement in phase space of the action variables (related to the elliptic elements of the minor body) for an exponentially long time. As a concrete application. we selected the Sun-Ceres-Jupiter case, obtaining (after the proper normal form reduction) a stability result for a time comparable to the age of the solar system (i.e., 4.9 · 109 years) and for a mass ratio of the primaries less or equal than 10–6. 相似文献