共查询到20条相似文献，搜索用时 31 毫秒
1.
Yoshio Kubo 《Celestial Mechanics and Dynamical Astronomy》2011,110(2):143-168
Under perturbations from outer bodies, the Earth experiences changes of its angular momentum axis, figure axis and rotational
axis. In the theory of the rigid Earth, in addition to the precession and nutation of the angular momentum axis given by the
Poisson terms, both the figure axis and the rotational axis suffer forced deviation from the angular momentum axis. This deviation
is expressed by the so-called Oppolzer terms describing separation of the averaged figure axis, called CIP (Celestial Intermediate
Pole) or CEP (Celestial Ephemeris Pole), and the mathematically defined rotational axis, from the angular momentum axis. The
CIP is the rotational axis in a frame subject to both precession and nutation, while the mathematical rotational axis is that
in the inertial (non-rotating) frame. We investigate, kinematically, the origin of the separation between these two axes—both
for the rigid Earth and an elastic Earth. In the case of an elastic Earth perturbed by the same outer bodies, there appear
further deviations of the figure and rotational axes from the angular momentum axis. These deviations, though similar to the
Oppolzer terms in the rigid Earth, are produced by quite a different physical mechanism. Analysing this mechanism, we derive
an expression for the Oppolzer-like terms in an elastic Earth. From this expression we demonstrate that, under a certain approximation
(in neglect of the motion of the perturbing outer bodies), the sum of the direct and convective perturbations of the spin
axis coincides with the direct perturbation of the figure axis. This equality, which is approximate, gets violated when the
motion of the outer bodies is taken into account. 相似文献
2.
Gravity-gradient perturbations of the attitude motion of a tumbling tri-axial satellite are investigated. The satellite center of mass is considered to be in an elliptical orbit about a spherical planet and to be tumbling at a frequency much greater than orbital rate. In determining the unperturbed (free) motion of the satellite, a canonical form for the solution of the torque-free motion of a rigid body is obtained. By casting the gravity-gradient perturbing torque in terms of a perturbing Hamiltonian, the long-term changes in the rotational motion are derived. In particular, far from resonance, there are no long-period changes in the magnitude of the rotational angular momentum and rotational energy, and the rotational angular momentum vector precesses abound the orbital angular momentum vector.At resonance, a low-order commensurability exists between the polhode frequency and tumbling frequency. Near resonance, there may be small long-period fluctuations in the rotational energy and angular momentum magnitude. Moreover, the precession of the rotational angular momentum vector about the orbital angular momentum vector now contains substantial long-period contributions superimposed on the non-resonant precession rate. By averaging certain long-period elliptic functions, the mean value near resonance for the precession of the rotational angular momentum vector is obtained in terms of initial conditions. 相似文献
3.
Marcello Romano 《Celestial Mechanics and Dynamical Astronomy》2008,101(4):375-390
New exact analytic solutions are introduced for the rotational motion of a rigid body having two equal principal moments of
inertia and subjected to an external torque which is constant in magnitude. In particular, the solutions are obtained for
the following cases: (1) Torque parallel to the symmetry axis and arbitrary initial angular velocity; (2) Torque perpendicular
to the symmetry axis and such that the torque is rotating at a constant rate about the symmetry axis, and arbitrary initial
angular velocity; (3) Torque and initial angular velocity perpendicular to the symmetry axis, with the torque being fixed
with the body. In addition to the solutions for these three forced cases, an original solution is introduced for the case
of torque-free motion, which is simpler than the classical solution as regards its derivation and uses the rotation matrix
in order to describe the body orientation. This paper builds upon the recently discovered exact solution for the motion of
a rigid body with a spherical ellipsoid of inertia. In particular, by following Hestenes’ theory, the rotational motion of
an axially symmetric rigid body is seen at any instant in time as the combination of the motion of a “virtual” spherical body
with respect to the inertial frame and the motion of the axially symmetric body with respect to this “virtual” body. The kinematic
solutions are presented in terms of the rotation matrix. The newly found exact analytic solutions are valid for any motion
time length and rotation amplitude. The present paper adds further elements to the small set of special cases for which an
exact solution of the rotational motion of a rigid body exists. 相似文献
4.
Efi Meletlidou Simos Ichtiaroglou Fabian Josef Winterberg 《Celestial Mechanics and Dynamical Astronomy》2001,80(2):145-156
We prove that Hill's lunar problem does not possess a second analytic integral of motion, independent of the Hamiltonian. In order to obtain this result, we avoid the usual normalization in which the angular velocity of the rotating reference frame is put equal to unit. We construct an artificial Hamiltonian that includes an arbitrary parameter b and show that this Hamiltonian does not possess an analytic integral of motion for in an open interval around zero. Then, by selecting suitable values of , b and using the invariance of the Hamiltonian under scaling in the units of length and time, we show that the Hamiltonian of Hill's problem does not possess an integral of motion, analytically continued from the integrable two–body problem in a rotating frame. 相似文献
5.
E. Schmutzer 《Astronomische Nachrichten》2006,327(1):29-35
In a previous paper we treated within the framework of our Projective Unified Field Theory (Schmutzer 2004, 2005a) the 2‐body system (e.g. Earth‐Moon system) with a rotating central body in a rather abstract manner. Here a concrete model of the transfer of angular momentum from the rotating central body to the orbital motion of the whole 2‐body system is presented, where particularly the transfer is caused by the inhomogeneous gravitational force of the Moon acting on the oceanic waters of the Earth, being modeled by a spherical shell around the solid Earth. The theory is numerically tested. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
6.
Starting from the Hamiltonian model for a solid Earth with an elastic mantle previously developped by the authors, analytical expressions are derived which give the nutation series corresponding to the plane perpendicular to the angular momentum vector, to the plane perpendicular to the rotational axis and to the equator of figure, as well as the series that give the polar motion. The effects of the different perturbations — solid Earth, centrifugal and tidal potentials — are calculated separately. The corrections due to the elasticity of the mantle, which mostly correspond to the Oppolzer terms, are calculated with an accuracy of 10–6 arc sec., given that the intrinsic observational accuracy has reached 0.01 mas. 相似文献
7.
B. P. Kondratyev 《Solar System Research》2013,47(1):1-10
A two-component theoretical model of the physical libration of the Moon in longitude is constructed with account taken of the viscosity of the core. In the new version, a hydrodynamic problem of motion of a fluid filling a solid rotating shell is solved. It is found that surfaces of equal angular velocity are spherical, and a velocity field of the fluid core of the Moon is described by elementary functions. A distribution of the internal pressure in the core is found. An angular momentum exchange between the fluid core and solid mantle is described by a third-order differential equation with a right-hand side. The roots of a characteristic equation are studied and the stability of rotation is proved. A libration angle as a function of time is found using the derived solution of the differential equation. Limiting cases of infinitely large and infinitely small viscosity are considered and an effect of lag of a libration phase from a phase of action of an external moment of forces is ascertained. This makes it possible to estimate the viscosity and sizes of the lunar fluid core from data of observations. 相似文献
8.
V. V. Beletskii 《Celestial Mechanics and Dynamical Astronomy》1972,6(3):356-378
Celestial body rotation about its center of mass, taking into account the body orbit evolution, is considered. Non-linear evolution equations of motion are constructed. Empirical Cassini's laws describing the Moon motion result from these equations as their stationary points. Bifurcation conditions of steady motions are written out and conditions of their stability are investigated. Hypothesis of Mercury's resonance motion analogous to the motion by Cassini is discussed. Consequences of this hypothesis are considered.The first information including the results mentioned in the paper was previously published in preprint [1]. 相似文献
9.
Two-integral distribution functions for axisymmetric systems 总被引：1，自引：0，他引：1
Zhenglu Jiang Leonid Ossipkov 《Monthly notices of the Royal Astronomical Society》2007,379(3):1133-1142
Some formulae are presented for finding two-integral distribution functions (DFs) which depend only on the two classical integrals of the energy and the magnitude of the angular momentum with respect to the axis of symmetry for stellar systems with known axisymmetric densities. They come from a combination of the ideas of Eddington and Fricke and they are also an extension of those shown by Jiang and Ossipkov for finding anisotropic DFs for spherical galaxies. The density of the system is required to be expressed as a sum of products of functions of the potential and of the radial coordinate. The solution corresponding to this type of density is in turn a sum of products of functions of the energy and of the magnitude of the angular momentum about the axis of symmetry. The product of the density and its radial velocity dispersion can be also expressed as a sum of products of functions of the potential and of the radial coordinate. It can be further known that the density multiplied by its rotational velocity dispersion is equal to a sum of products of functions of the potential and of the radial coordinate minus the product of the density and the square of its mean rotational velocity. These formulae can be applied to the Binney and the Lynden-Bell models. An infinity of the odd DFs for the Binney model can be also found under the assumption of the laws of the rotational velocity. 相似文献
10.
G. P. Horedt 《Astrophysics and Space Science》1978,54(2):253-261
We discuss the rotation of interstellar clouds which are in a stage immediately before star formation. Cloud collisions seem to be the principal cause of the observed rotation of interstellar clouds. The rotational motion of the clouds is strongly influenced by turbulence.Theories dealing with the resolution of the angular momentum problem in star formation are classified into five major groups. We develop the old idea that the angular momentum of an interstellar cloud passes during star formation into the angular momentum of double star systems and/or circumstellar clouds.It is suggested that a rotating gas cloud contracts into a ring-like structure which fragments into self-gravitating subcondensations. By collisions and gas accretion these subcondensations accrete into binary systems surrounded by circumstellar clouds. Using some rough approximations we find analytical expressions for the semi-major axis of the binary system and for the density of the circumstellar clouds as a function of the initial density and of the initial angular velocity of an interstellar cloud. The obtained values are well within the observational limits. 相似文献
11.
We study the dynamical interactions of mass systems in equilibrium under their own gravity that mutually exert and ex‐perience gravitational forces. The method we employ is to model the dynamical evolution of two isolated bars, hosted within the same galactic system, under their mutual gravitational interaction. In this study, we present an analytical treatment of the secular evolution of two bars that oscillate with respect to one another. Two cases of interaction, with and without geometrical deformation, are discussed. In the latter case, the bars are described as modified Jacobi ellipsoids. These triaxial systems are formed by a rotating fluid mass in gravitational equilibrium with its own rotational velocity and the gravitational field of the other bar. The governing equation for the variation of their relative angular separation is then numerically integrated, which also provides the time evolution of the geometrical parameters of the bodies. The case of rigid, non‐deformable, bars produces in some cases an oscillatory motion in the bodies similar to that of a harmonic oscillator. For the other case, a deformable rotating body that can be represented by a modified Jacobi ellipsoid under the influence of an exterior massive body will change its rotational velocity to escape from the attracting body, just as if the gravitational torque exerted by the exterior body were of opposite sign. Instead, the exchange of angular momentum will cause the Jacobian body to modify its geometry by enlarging its long axis, located in the plane of rotation, thus decreasing its axial ratios. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
12.
Walter Petry 《Astrophysics and Space Science》1991,175(1):1-14
The study of a previously proposed theory of gravitation in flat space-time (Petry, 1981a) is continued. A conservation law for the angular momentum is derived. Additional to the usual form, there must be added a term coming from the spin of the gravitational field. The equations of motion and of spin angular momentum for a spinning test particle in a gravitational field are given. An approximation of the equations of the spin angular momentum in the rest frame of the test particle is studied. For a gyroscope in an orbit of a rotating massive body (e.g., the Earth) the precession of the spin axis agrees with the result of Einstein's general theory of relativity. 相似文献
13.
Jeffrey M. Cohen 《Astrophysics and Space Science》1970,6(2):263-274
In this paper we give general relativistic expressions for the angular momentum and rotational kinetic energy of slowly rotating stars. These expressions contain contributions from the presure, gravitational red shift, and Doppler shift, and the motion of inertial frames. These contributions are not negligible, e.g., there are stable neutron star models for which the angular velocity of inertial frames at the center is about 70% the angular velocity of the star. These expressions are useful in the study of pulsars if pulsars are rotating neutron stars. 相似文献
14.
We construct an explicit reversible symplectic integrator for the planar 3-body problem with zero angular momentum. We start with a Hamiltonian of the planar 3-body problem that is globally regularised and fully symmetry reduced. This Hamiltonian is a sum of 10 polynomials each of which can be integrated exactly, and hence a symplectic integrator is constructed. The performance of the integrator is examined with three numerical examples: The figure eight, the Pythagorean orbit, and a periodic collision orbit. 相似文献
15.
Joseph J. F. Liu Philip M. Fitzpatrick 《Celestial Mechanics and Dynamical Astronomy》1975,12(4):463-487
Differential equations are derived for studying the effects of either conservative or nonconservative torques on the attitude motion of a tumbling triaxial rigid satellite. These equations, which are analogous to the Lagrange planetary equations for osculating elements, are then used to study the attitude motions of a rapidly spinning, triaxial, rigid satellite about its center of mass, which, in turn, is constrained to move in an elliptic orbit about an attracting point mass. The only torques considered are the gravity-gradient torques associated with an inverse-square field. The effects of oblateness of the central body on the orbit are included, in that, the apsidal line of the orbit is permitted to rotate at a constant rate while the orbital plane is permitted to precess (either posigrade or retrograde) at a constant rate with constant inclination.A method of averaging is used to obtain an intermediate set of averaged differential equations for the nonresonant, secular behavior of the osculating elements which describe the complete rotational motions of the body about its center of mass. The averaged differential equations are then integrated to obtain long-term secular solutions for the osculating elements. These solutions may be used to predict both the orientation of the body with respect to a nonrotating coordinate system and the motion of the rotational angular momentum about the center of mass. The complete development is valid to first order in (n/w
0)2, wheren is the satellite's orbital mean motion andw
0 its initial rotational angular speed. 相似文献
16.
Alberto Escapa 《Celestial Mechanics and Dynamical Astronomy》2011,110(2):99-142
We explore the evolution of the angular velocity of an elastic Earth model, within the Hamiltonian formalism. The evolution
of the rotation state of the Earth is caused by the tidal deformation exerted by the Moon and the Sun. It can be demonstrated
that the tidal perturbation to spin depends not only upon the instantaneous orientation of the Earth, but also upon its instantaneous
angular velocity. Parameterizing the orientation of the Earth figure axis with the three Euler angles, and introducing the
canonical momenta conjugated to these, one can then show that the tidal perturbation depends both upon the angles and the
momenta. This circumstance complicates the integration of the rotational motion. Specifically, when the integration is carried
out in terms of the canonical Andoyer variables (which are the rotational analogues to the orbital Delaunay variables), one
should keep in mind the following subtlety: under the said kind of perturbations, the functional dependence of the angular
velocity upon the Andoyer elements differs from the unperturbed dependence (Efroimsky in Proceedings of Journées 2004: Systèmes
de référence spatio-temporels. l’Observatoire de Paris, pp 74–81, 2005; Efroimsky and Escapa in Celest. Mech. Dyn. Astron. 98:251–283, 2007). This happens because, under angular velocity dependent perturbations, the requirement for the Andoyer elements to be canonical
comes into a contradiction with the requirement for these elements to be osculating, a situation that parallels a similar
antinomy in orbital dynamics. Under the said perturbations, the expression for the angular velocity acquires an additional
contribution, the so called convective term. Hence, the time variation induced on the angular velocity by the tidal deformation
contains two parts. The first one comes from the direct terms, caused by the action of the elastic perturbation on the torque-free
expressions of the angular velocity. The second one arises from the convective terms. We compute the variations of the angular
velocity through the approach developed in Getino and Ferrándiz (Celest. Mech. Dyn. Astron. 61:117–180, 1995), but considering the contribution of the convective terms. Specifically, we derive analytical formulas that determine the
elastic perturbations of the directional angles of the angular velocity with respect to a non-rotating reference system, and
also of its Cartesian components relative to the Tisserand reference system of the Earth. The perturbation of the directional
angles of the angular velocity turns out to be different from the evolution law found in Kubo (Celest. Mech. Dyn. Astron.
105:261–274, 2009), where it was stated that the evolution of the angular velocity vector mimics that of the figure axis. We investigate comprehensively
the source of this discrepancy, concluding that the difference between our results and those obtained in Ibid. stems from an oversimplification made by Kubo when computing the direct terms. Namely, in his computations Kubo disregarded
the motion of the tide raising bodies with respect to a non-rotating reference system when compared with the Earth rotational
motion. We demonstrate that, from a numerical perspective, the convective part provides the principal contribution to the
variation of the directional angles and of length of day. In the case of the x and y components in the Tisserand system, the convective contribution is of the same order of magnitude as the direct one. Finally,
we show that the approximation employed in Kubo (Ibid.) leads to significant numerical differences at the level of a hundred micro-arcsecond. 相似文献
17.
Benoît Noyelles 《Icarus》2009,202(1):225-239
The rotation of the main natural satellites of the Solar System is widely assumed to be synchronous, because this corresponds to an equilibrium state. In the case of the Moon, 3 laws have been formulated by Cassini, assuming a spin-orbit resonance and a 1:1 nodal resonance. The recent gravitational data collected by the spacecrafts Galileo (in the jovian system) and Cassini (in the saturnian system) allows us to study the rotation of other natural satellites, and to check the universality of Cassini's laws. This paper deals with the rotation of the Galilean satellites of Jupiter J-4 Callisto. In this study we use both analytical (like Lie transforms) and numerical methods (numerical detection of chaos, numerical integration, frequency analysis) to first check the reliability of Cassini Laws for Callisto, and then to give a first theory of its rotation, Callisto's being considered as a rigid body. We first show that the Third Cassini Law (i.e. the nodal resonance), is not satisfied in every reference frame, in particular in the most natural one (i.e. the J2000 jovian equator). The difference of the nodes presents a chaotic-like behavior, that we prove to be just a geometrical illusion. Moreover, we give a mathematical condition ruling the choice of an inertial reference frame in which the Third Cassini Law is fulfilled. Secondly, we give a theory of Callisto's rotation in the International Celestial Reference Frame (ICRF). We highlight a small motion (i.e. <200 m) of its rotation axis about its body figure, a 11.86-yr periodicity in Callisto's length-of-day, and the proximity of a resonance that forces 182-yr librations in Callisto's obliquity. 相似文献
18.
J2 Invariant Relative Orbits for Spacecraft Formations 总被引：1，自引：0，他引：1
An analytic method is presented to establish J
2 invariant relative orbits. Working with mean orbit elements, the secular drift of the longitude of the ascending node and the sum of the argument of perigee and mean anomaly are set equal between two neighboring orbits. By having both orbits drift at equal angular rates on the average, they will not separate over time due to the J2 influence. Two first order conditions are established between the differences in momenta elements (semi-major axis, eccentricity and inclination angle) that guarantee that the drift rates of two neighboring orbits are equal on the average. Differences in the longitude of the ascending node, argument of perigee and initial mean anomaly can be set at will, as long as they are setup in mean element space. For near polar orbits, enforcing both momenta element constraints may result in impractically large relative orbits. It this case it is shown that dropping the equal ascending node rate requirement still avoids considerable relative orbit drift and provides substantial fuel savings.This revised version was published online in October 2005 with corrections to the Cover Date. 相似文献
19.
The secular effect of YORP torque on the rotational dynamics of an asteroid in non-principal axis rotation is studied. The
general rotational equations of motion are derived and approximated with an illumination function expanded up to second order.
The resulting equations of motion can be averaged over the fast rotation angles to yield secular equations for the angular
momentum, dynamic inertia and obliquity. We study the properties of these secular equations and compare results to previous
research. Finally, an application to several real asteroid shapes is made, in particular we study the predicted rotational
dynamics of the asteroid Toutatis, which is known to be in a non-principal axis state. 相似文献
20.
We have investigated the effects of increasing optical depths on spectral lines formed in a rotating and expanding spherical
shell. We have assumed a shell whose outer radius is 3 times the inner radius, with the radial optical depths equal to 10,
50, 100, 500. We have employed a constant velocity with no velocity gradients in the shell. The shell is assumed to be rotating
with velocities varying as 1/ρ, whereρ is the perpendicular distance from the axis of rotation, implying the conservation of angular momentum. Two expansion (radial)
velocities are treated: (1)V = 0 (static case) and (2)V = 10 mean thermal units. The maximum rotational velocities areV
rot = 0, 5, 10 and 20. In the shell where there are no radial motions, we obtain symmetric lines with emission in the wings forV
rot = 0 and 5 while forV
rot ≥ 10 we obtain symmetric absorption lines. In the case of an expanding shell, we obtain lines with central emission. 相似文献