共查询到20条相似文献，搜索用时 31 毫秒
1.
Off-center vector magnetograms which use all three components of the measured field provide the maximum information content from the photospheric field and can provide the most consistent potential field independent of the viewing angle by defining the normal component of the field. The required transformations of the magnetic field vector and the geometric mapping of the observed field in the image plane into the heliographic plane have been described. Here we discuss the total transformation of specific vector magnetograms to detail the problems and procedures that one should be aware of in analyzing observational magnetograms. The effect of the 180-deg ambiguity of the observed transverse field is considered as well as the effect of curvature of the photosphere. Specific results for active regions AR 2684 (23 September, 1980) and AR 4474 (26 April, 1984) from the Marshall Space Flight Center Vector Magnetograph are described which point to the need for the heliographic projection in determining the field structure of an active region. 相似文献
2.
Zhen Yang Yazhong Luo Jin Zhang Hengnian Li 《Celestial Mechanics and Dynamical Astronomy》2018,130(9):56
This paper develops a nonlinear analytic solution for satellite relative motion in J2-perturbed elliptic orbits by using the geometric method that can avoid directly solving the complex differential equations. The differential equinoctial elements (DEEs) are used to remove any singularities for zero-eccentricity or zero-inclination orbits. Based on the relationship between the relative states and the DEEs, state transition tensors (STTs) for transforming the osculating DEEs and propagating the mean DEEs have been derived. The formulation of these STTs has been split into a set of vector and matrix operations, which avoids directly expanding the complex second-order terms, and thus, the obtained STTs could be easy-to-understand and easy-to-code. Numerical results show that the proposed nonlinear solution is valid for zero-eccentricity and zero-inclination reference orbit and is more accurate than the previous linear or nonlinear methods for the long-term prediction of satellite relative motion. 相似文献
3.
R. M. Weisman M. Majji K. T. Alfriend 《Celestial Mechanics and Dynamical Astronomy》2014,118(2):165-195
This paper presents an approach to characterize the uncertainty associated with the state vector obtained from the Herrick-Gibbs orbit determination approach using transformation of variables. The approach is applied to estimate the state vector and its probability density function for objects in low Earth orbit using sparse observations. The state vector and associated uncertainty estimates are computed in Cartesian coordinates and Keplerian elements. The approach is then extended to accommodate the $J_2$ perturbation where the state vector is written in terms of mean orbital elements. The results obtained from the analytical approach presented in this paper are validated using Monte Carlo simulations and compared with the often utilized similarity transformation for Kepler, mean, and nonsingular elements. The measurement uncertainty characterization obtained is used to initialize conventional nonlinear filters as well as operate a Bayesian approach for orbit determination and object tracking. 相似文献
4.
Paul E. Nacozy 《Celestial Mechanics and Dynamical Astronomy》1981,23(2):173-198
Time elements are introduced in terms of Keplerian (classical) orbital elements for use with time transformations of the Sundman type. Three different time elements are introduced. One time element is associated with the eccentric anomaly, a second time element is associated with the true anomaly, and a third time element is associated with theintermediate anomaly.Numerical results are presented that show accuracy improvements of from one to two orders of magnitude when time elements are employed along with Sundman time transformations, compared with using time transformations alone. 相似文献
5.
M. A. Vashkov’yak 《Astronomy Letters》2005,31(1):64-72
We describe an approximate numerical-analytical method for calculating the perturbations of the elements of distant satellite orbits. The model for the motion of a distant satellite includes the solar attraction and the eccentricity and ecliptic inclination of the orbit of the central planet. In addition, we take into account the variations in planetary orbital elements with time due to secular perturbations. Our work is based on Zeipel’s method for constructing the canonical transformations that relate osculating satellite orbital elements to the mean ones. The corresponding transformation of the Hamiltonian is used to construct an evolution system of equations for mean elements. The numerical solution of this system free from rapidly oscillating functions and the inverse transformation from the mean to osculating elements allows the evolution of distant satellite orbits to be studied on long time scales on the order of several hundred or thousand satellite orbital periods. 相似文献
6.
Michel Rapaport 《Celestial Mechanics and Dynamical Astronomy》1980,21(2):177-182
We use classical definitions and results of differential geometry in studying properties of transformations depending on a small parameter, acting on differential systems.Notions of one-parameter Lie's group of transformations, of bracket of vector fields (Lie's derivative) ard used. In the same way, the notion of symplectic manifold and of transformations which keep invariant a 2-form are useful.Proceedings of the Sixth Conference on Mathematical Methods in Celestial Mechanics held at Oberwolfach (West Germany) from 14 to 19 August, 1978. 相似文献
7.
Poincaré designed the méthode nouvelle in order to build approximate integrals of Hamiltonians developed as series of a small
parameter. Due to several critical deficiencies, however, the method has fallen into disuse in favor of techniques based on
Lie transformations. The paper shows how to repair these shortcomings in order to give Poincaré’s méthode nouvelle the same
functionality as the Lie transformations. This is done notably with two new operations over power series: a skew composition
to expand series whose coefficients are themselves series, and a skew reversion to solve implicit vector equations involving
power series. These operations generalize both Arbogast’s technique and Lagrange’s inversion formula to the fullest extent
possible.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
8.
P. Pástor 《Celestial Mechanics and Dynamical Astronomy》2012,112(1):23-45
The orbital evolution of a dust particle under the action of a fast interstellar gas flow is investigated. The secular time
derivatives of Keplerian orbital elements and the radial, transversal, and normal components of the gas flow velocity vector
at the pericentre of the particle’s orbit are derived. The secular time derivatives of the semi-major axis, eccentricity,
and of the radial, transversal, and normal components of the gas flow velocity vector at the pericentre of the particle’s
orbit constitute a system of equations that determines the evolution of the particle’s orbit in space with respect to the
gas flow velocity vector. This system of differential equations can be easily solved analytically. From the solution of the
system we found the evolution of the Keplerian orbital elements in the special case when the orbital elements are determined
with respect to a plane perpendicular to the gas flow velocity vector. Transformation of the Keplerian orbital elements determined
for this special case into orbital elements determined with respect to an arbitrary oriented plane is presented. The orbital
elements of the dust particle change periodically with a constant oscillation period or remain constant. Planar, perpendicular
and stationary solutions are discussed. The applicability of this solution in the Solar System is also investigated. We consider
icy particles with radii from 1 to 10 μm. The presented solution is valid for these particles in orbits with semi-major axes
from 200 to 3000 AU and eccentricities smaller than 0.8, approximately. The oscillation periods for these orbits range from
105 to 2 × 106 years, approximately. 相似文献
9.
Samuel P. Altman 《Celestial Mechanics and Dynamical Astronomy》1975,11(4):405-428
The orbital state of a satellite in a central force field can be uniquely described by its velocity hodograph, a circle, rather than the Keplerian conic. Also, its coordinate-frame rotation about the attracting center is definable, without singularity, by the four-parameter set of Euler parameters. A unified state model of orbital trajectory and attitude dynamics has previously been developed by use of state variables of the orbital velocity hodograph and Euler parameters. The dynamical constraint equations of this orbital state model are especially effective in advanced techniques of state estimation, used for orbit determination and prediction. External observations of orbital vehicles, such as provided by optical and radar sensors of tracking systems, are transformable into corresponding velocity state maps, as presented in this paper. These transformations and the consequent state maps are essential for development of the orbit observation matrix used with the unified state matrix, in recursive estimators such as the Kalman filters. Line-of-sight rays and range spheres (or hemispheres) of observations map conformally into orthogonal spherical surfaces in velocity space, as the result of the point-contact transformations. In bispherical coordinates, the field of observation maps for a ground-based tracking system site is shown to be a reduced (or degenerate) form of the general field of observation maps for a satellite-based tracking site. These orbital state maps and transforms are directly useful in development of observation matrices for candidate observation sets, such as range only, angle only, or range plus range-rate tracking schemes. Also, surface coverage patterns can be generated for proposed new tracking systems, in mission analysis and system synthesis studies. 相似文献
10.
A new nonsingular analytical theory for the motion of near Earth satellite orbits with the air drag effect is developed for long term motion in terms of the KS uniformly regular canonical elements by a series expansion method, by assuming the atmosphere to be symmetrically spherical with constant density scale height. The series expansions include up to third order terms in eccentricity. Only two of the nine equations are solved analytically to compute the state vector and change in energy at the end of each revolution, due to symmetry in the equations of motion. Numerical comparisons of the important orbital parameters semi major axis and eccentricity up to 1000 revolutions, obtained with the present solution, with KS elements analytical solution and Cook, King-Hele and Walker's theory with respect to the numerically integrated values, show the superiority of the present solution over the other two theories over a wide range of eccentricity, perigee height and inclination. 相似文献
11.
Gang-Wei Wang Tian-Zhou Xu Stephen Johnson Anjan Biswas 《Astrophysics and Space Science》2014,349(1):317-327
In this paper, complete geometric symmetry of extended quantum Zakharov–Kuznetsov (QZK) equation are investigated. All of the geometric vector fields for the new extended QZK equation are presented. At the same time, a plethora of exact solutions are obtained by the application of the group theorem. In addition, 1-soliton solution of the extended QZK equation with power law nonlinearity is obtained by the aid of traveling wave hypothesis with the necessary constraints in place for the existence of the soliton. 相似文献
12.
The Lie transform method used in Perturbation Theory is based upon an intrinsic algorithm for transforming functions or vector fields by a transformation close to the identity. It can thus be viewed as a specialization of methods and results of differential geometry as is shown in the first part of this paper. In a second part we answer some of the questions left open in connection with the equivalence of the algorithms proposed by Hori and Deprit. From a formal point of view, the methods are shown to be equivalent for non-canonical as well as canonical transformations and a formula relating directly the two generating functions (or vector fields) is presented (formula (5.17)). On the other hand, the equivalence is shown to hold also in the ring ofp-differentiable functions. 相似文献
13.
Christian Circi Ennio Condoleo Emiliano Ortore 《Celestial Mechanics and Dynamical Astronomy》2017,128(2-3):361-382
Taking into consideration a probe moving in an elliptical orbit around a celestial body, the possibility of determining conditions which lead to constant values on average of all the orbit elements has been investigated here, considering the influence of the planetary oblateness and the long-term effects deriving from the attraction of several perturbing bodies. To this end, three equations describing the variation of orbit eccentricity, apsidal line and angular momentum unit vector have been first retrieved, starting from a vectorial expression of the Lagrange planetary equations and considering for the third-body perturbation the gravity-gradient approximation, and then exploited to demonstrate the feasibility of achieving the above-mentioned goal. The study has led to the determination of two families of solutions at constant mean orbit elements, both characterised by a co-planarity condition between the eccentricity vector, the angular momentum and a vector resulting from the combination of the orbital poles of the perturbing bodies. As a practical case, the problem of a probe orbiting the Moon has been faced, taking into account the temporal evolution of the perturbing poles of the Sun and Earth, and frozen solutions at argument of pericentre 0\(^{\circ }\) or 180\(^{\circ }\) have been found. 相似文献
14.
《Planetary and Space Science》2007,55(10):1388-1397
A new non-singular analytical theory for the motion of near Earth satellite orbits with the air drag effect is developed in terms of the Kustaanheimo and Stiefel (KS) uniformly regular canonical elements, by assuming the atmosphere to be oblate diurnally varying with constant density scale height. The series expansions include up to third-order terms in eccentricity and c (a small parameter dependent on the flattening of the atmosphere). Only two of the nine equations are solved analytically to compute the state vector and change in energy at the end of each revolution, due to symmetry in the equations of motion. Numerical comparisons of the important orbital parameters semimajor axis and eccentricity up to 1000 revolutions, obtained with the present solution, with the third-order analytical theories of Swinerd and Boulton and in terms of the KS elements, with respect to the numerically integrated values, show the superiority of the present solution over the other two theories over a wide range of eccentricity, perigee height and inclination. 相似文献
15.
Theory of the motion of an artificial Earth satellite 总被引：1，自引：0，他引：1
Felix R. Hoots 《Celestial Mechanics and Dynamical Astronomy》1981,23(4):307-363
An improved analytical solution is obtained for the motion of an artificial Earth satellite under the combined influences of gravity and atmospheric drag. The gravitational model includes zonal harmonics throughJ
4, and the atmospheric model assumes a nonrotating spherical power density function. The differential equations are developed through second order under the assumption that the second zonal harmonic and the drag coefficient are both first-order terms, while the remaining zonal harmonics are of second order.Canonical transformations and the method of averaging are used to obtain transformations of variables which significantly simplify the transformed differential equations. A solution for these transformed equations is found; and this solution, in conjunction with the transformations cited above, gives equations for computing the six osculating orbital elements which describe the orbital motion of the satellite. The solution is valid for all eccentricities greater than 0 and less than 0.1 and all inclinations not near 0o or the critical inclination. Approximately ninety percent of the satellites currently in orbit satisfy all these restrictions. 相似文献
16.
Aaron J. Rosengren Daniel J. Scheeres 《Celestial Mechanics and Dynamical Astronomy》2014,118(3):197-220
We consider sets of natural vectorial orbital elements of the Milankovitch type for perturbed Keplerian motion. These elements are closely related to the two vectorial first integrals of the unperturbed two-body problem; namely, the angular momentum vector and the Laplace–Runge–Lenz vector. After a detailed historical discussion of the origin and development of such elements, nonsingular equations for the time variations of these sets of elements under perturbations are established, both in Lagrangian and Gaussian form. After averaging, a compact, elegant, and symmetrical form of secular Milankovitch-like equations is obtained, which reminds of the structure of canonical systems of equations in Hamiltonian mechanics. As an application of this vectorial formulation, we analyze the motion of an object orbiting about a planet (idealized as a point mass moving in a heliocentric elliptical orbit) and subject to solar radiation pressure acceleration (obeying an inverse-square law). We show that the corresponding secular problem is integrable and we give an explicit closed-form solution. 相似文献
17.
Vinti’s potential is revisited for analytical propagation of the main satellite problem, this time in the context of relative motion. A particular version of Vinti’s spheroidal method is chosen that is valid for arbitrary elliptical orbits, encapsulating \(J_2\), \(J_3\), and generally a partial \(J_4\) in an orbit propagation theory without recourse to perturbation methods. As a child of Vinti’s solution, the proposed relative motion model inherits these properties. Furthermore, the problem is solved in oblate spheroidal elements, leading to large regions of validity for the linearization approximation. After offering several enhancements to Vinti’s solution, including boosts in accuracy and removal of some singularities, the proposed model is derived and subsequently reformulated so that Vinti’s solution is piecewise differentiable. While the model is valid for the critical inclination and nonsingular in the element space, singularities remain in the linear transformation from Earth-centered inertial coordinates to spheroidal elements when the eccentricity is zero or for nearly equatorial orbits. The new state transition matrix is evaluated against numerical solutions including the \(J_2\) through \(J_5\) terms for a wide range of chief orbits and separation distances. The solution is also compared with side-by-side simulations of the original Gim–Alfriend state transition matrix, which considers the \(J_2\) perturbation. Code for computing the resulting state transition matrix and associated reference frame and coordinate transformations is provided online as supplementary material. 相似文献
18.
G. Scheifele 《Celestial Mechanics and Dynamical Astronomy》1970,2(3):296-310
Generalizations in the canonical theory of dynamics are made; at first transformations which augment the number of canonical variables, and secondly differential transformations of the independent variable are outlined. This is applied to the perturbed two-body problem. The results are canonical systems using independent variables other than time. This leads to Delaunay-similar sets of 8 canonical elements when the Jacobian equation is separable. The application of the theory to the KS-transformation yields a completely regular canonical system in a 10-dimensional phase-space, using the eccentric anomaly as independent variable. Subsequently sets of 10 regular canonical elements are introduced.Presented at the Conference on Celestial Mechanics, Oberwolfach, Germany, August 17–23, 1969. 相似文献
19.
Ram Krishan Sharma 《Celestial Mechanics and Dynamical Astronomy》1993,56(4):503-521
Analytical theory for short-term orbit motion of satellite orbits with Earth's zonal harmonicsJ
3 andJ
4 is developed in terms of KS elements. Due to symmetry in KS element equations, only two of the nine equations are integrated analytically. The series expansions include terms of third power in the eccentricity. Numerical studies with two test cases reveal that orbital elements obtained from the analytical expressions match quite well with numerically integrated values during a revolution. Typically for an orbit with perigee height, eccentricity and inclination of 421.9 km, 0.17524 and 30 degrees, respectively, maximum differences of 27 and 25 cm in semimajor axis computation are noted withJ
3 andJ
4 term during a revolution. For application purposes, the analytical solutions can be used for accurate onboard computation of state vector in navigation and guidance packages. 相似文献
20.
A set of differential equations is derived that has a number of advantages in special perturbation work. In particular, the equations remain valid for all values of the orbital eccentricity and inclination including zero. They are therefore applicable to parabolic- and hyperbolic-type orbits as well as elliptic-type; a scheme for use when the orbit is rectilinear or nearly so is provided. The equations are also much simpler in form than the Lagrange planetary equations and the transformations of the osculating elements to and from the rectangular coordinates are straightforward. 相似文献