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Motion equations for the gravitationally coupled orbit-attitude motion of a spacecraft are presented. The gravitational force and torque are expanded in a Taylor series in the small ratio (spacecraft size/orbital radius). A recursive definition for higher moments of inertia is introduced which permits terms up tofourth order to be retained. The expressions are fully nonlinear in the attitude variables. A quasi-sunpointing (QSP) passive attitude-control mode is used to assess the effects of higher moments of inertia and gravitational coupling. The attitude motion is detectably coupled to the orbital motion. However, the higher moments of inertia influence only the attitude motion.Nomenclature f G ,g G ,f Gi ,g Gi total gravitational force and torque and their components of orderi in =/r 0 - angular momentum of spacecraft about 0 and the spacecraft mass center - J i ,I i general moment of inertia about 0 and the spacecraft mass center - second (dyadic), third (triadic), and fourth (tetradic) moment of inertia about 0 and the spacecraft mass center - A andB (and related components) of the second, third and fourth moments of inertia about 0, see Equation (9) - M, m Earth's mass, spacecraft mass - Q ba rotation matrix taking a into b - position vector from attracting body's mass center to a general mass element, to 0 and to the spacecraft mass center - 1, 2, 3 basis vectors of reference frame - , , N misalignment angle betweenb 3 and the (projected) true position of the Sun, its oscillatory component and nominal value - unit dyadic (-identity matrix) - ratio of characteristic spacecraft dimension to orbital radius - pitch angle (aboutb 2 axis) - Earth's gravitational parameter - , position vector from 0 to a general mass element and the spacecraft mass center - , the (projected) true longitude of the Sun and the true longitude of the spacecraft - / angular velocity of reference frame with respect to - (·), (*), (o) d()/dt with respect to inertial space I , and orbiting frame O and a body-fixed spacecraft frame b Presented at AAS/AIAA Astrodynamics Conference, Aug. 9–11, 1982.  相似文献   

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An anisotropic model with variableG and and bulk viscosity is considered. The model exhibits an inflationary behavior during which the coefficient of bulk viscosity varies lineraly with the energy density. This allows the anisotropy energy to decrease exponentially with time. Other results overlap with our earlier work with a different ansatz for . The gravitational constant was found to increase during the radiation and matter epochs.  相似文献   

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An analysis of the two-dimensional flow of water at 4°C past an infinite porous plate is presented, when the plate is subjected to a normal suction velocity and the heat flux at the plate is constant. Approximate solutions are derived for the velocity and temperature fields and the skin-friction. The effects ofG (Grashof number) andE (Eckert number) on the velocity and temperature fields are discussed.Nomenclature u, v velocity components of the fluid inx, y direction - g acceleration due to gravity - coefficient of thermal expansion of water at 4°C - v kinematic viscosity - density - T temperature inside thermal boundary layer - T free-stream temperature - k thermal conductivity - C p specific heat at constant pressure  相似文献   

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Einstein's equations of general relativity are solved in terms of gravitational potential derivatives, withT equal to mass and/or field energy such thatT 0 outside a body. The line element equation then describes the variance of test particle internal geometrical structure and time-rate due to work done in a field, not the space-time curvature. Specific properties of gravitational fields and bodies come from this new solution: (a) The gravitational field consists of electromagnetic spin 2 gravitons which produce the gravitational force through the magnetic vector. (b) The gravitational mass is the Newtonian mass, not the relativistic mass, of a moving body. (c) An action principle exists in gravitation theory. (d) Attractive gravity exists between matter and antimatter. (e) Unification with quantum physics appears possible.  相似文献   

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Summary Evolution of the orbital elements of a two-body system with slowly decreasing mass according to Jeans' mode is described by a non-linear, non-autonomous system of differential equations.In general the system contains one stationary solution (e=1,f=), for which an instability criterion is derived. For example the stationary solution is unstable for all Jeans-Eddington functionsm n (t) with 1n3 which characterize the loss of mass. Furthermore, it is possible to describe the quantitative behaviour ofE+,e anda for arbitrarym(t) in a large number of cases. In the case of the Jeans-Eddington functions we find that the amplitude of the oscillations ine is monotone decreasing with time ifn>3 and it is monotone increasing with time ifn<3.By comparing these analytical results with the numerical calculations of Hadjidemetriou we explain the rapid rotation of the line of apsides which occurs if the initial value ofe is nearly-circular.
, , . (e=1,f=), . , -m n (t), , 1n3. , E+,e a m(t) . - , , n>3, , n<3. , , - e.
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The high-frequency electromagnetic and gravitational radiation from a relativistic particle falling into a Kerr and Schwarzschild black hole is considered. The spectral and angular distributions of the radiation power are calculated by the WKB technique to Teukolsky's equations. The spectra obtained have a characteristic exponential cut-off at the frequency = char. which is proportional to the particle Lorentz factor =(1–v 2/c2)–1/2. At the frequencies as low as those compared with char. both electromagnetic and gravitational spectra are flat. The amount of the energy emitted in the low-frequency modes of the radiation depends strongly on the radiation spin. It is proportional to ln for the electromagnetic and to 3 for the gravitational radiation.  相似文献   

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Isentropic oscillations of a star in thermal imbalance are defined as those for which, at every istant, the entropy of each mass element of the configuration in the perturbed motion is equal to that of the same mass element in the unperturbed motion.The solution of the equations describing such isentropic oscillations and written in terms of the infinitesimal displacement r(r 0,t) is presented in terms of asymptotic expansions up to the first order in the parameter /t s where is the adiabatic pulsation period for the fundamental mode andt s , a slow time scale of the order of the Kelvin-Helmholtz time.The solution obtained allows one to define, unambiguously, an isentropic part to the coefficient of vibrational stability of arbitrary stellar models in thermal imbalance, as well as to derive a general formula relating the results of a stability analysis in terms of r and r/r.Application of this general solution to the simple case of homologous motion is also given.  相似文献   

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The gravity potential of an arbitrary bodyT is expanded in a series of spherical harmonics and rigorous evaluations of the general termV n of the expansion are obtained. It is proved thatV n decreases on the sphere envelopingT according to the power law if the body structure is smooth. For a body with analytic structure,V n decreases in geometric progression. The exactness of these evaluations is proved for bodies having irregular and analytic structures. For the terrestrial planetsV n =O (n –5/2).
I I V n IV n I . . IV n I . I. IV n =O(n –5/2 )
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In this paper we transform the wave equation governing gravitational perturbations of a Schwarzschild black hole from its standard Schrödinger or Regge-Wheeler form to a Klein-Gordon type wave equation. This latter form reveals immediately that incoming waves with frequencies () cml , a critical frequency, are completely reflected (transmitted). This process is entirely due to the radial variation of the cut-off frequency inherent in the dispersive nature of the wave propagation properties of gravitational perturbations of the Schwarzschild metric. Moreover, those high-frequency waves ( cml) which penetrate through the region near the Schwarzschild radiusr sare, on crossing this event horizon, attenuated by a factor exp (–r s/c), thereby dumping most of their energy and momentum into the black hole. It is shown that in the vicinity ofr sthe metric is locally unstable. This feature and the wave absorption process indicate that the neighbourhood aroundr sis dynamically active, and, as well as acting like a Hawking-type particle creator, will behave as a wave emitter in order to relax the stresses on the metric.  相似文献   

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Orbital stability of quasiperiodic motions in the many dimensional autonomic hamiltonian systems is considered. Studied motions are supposed to be not far from equilibrium, the number of their basic frequencies may be not equal to the number of degrees of freedom, and the procedure of their construction is supposed to be converged. The stability problem is solved in the strict nonlinear mode.Obtained results are used in the stability investigation of small plane motions near the lagrangian solutions of the three-dimensional circular restricted three-body problem. The values of parameters for which the plane motions are unstable have been found.
. , , . . , . , .
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Résumé Le présent travail est une continuation d'un autre, publié plus tôt (Doubochine, 1970). On montre ici, que les propriétés des mouvements Lagrangiens et Euleriens établies en mécanique céleste classique sont vraies aussi dans les cas plus généraux, envisagés dans le travail indiqué. On montre de plus, que les trajectoires des points en ces mouvements en axes absolus sont les spirales infinies s'enroulant sur les surfaces des cylindres curvilignes infinis.
-- , (, 1970). , , , , , , , . , , , , .
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The equations for the variation of the osculating elements of a satellite moving in an axi-symmetric gravitational field are integrated to yield the complete first-order perturbations for the elements of the orbit. The expressions obtained include the effects produced by the second to eighth spherical harmonics. The orbital elements are presented in the most general form of summations by means of Hansen coefficients. Due to their general forms it is a simple matter to estimate the perturbations of any higher harmonic by simply increasing the index of summation. Finally, this paper gives the respective general expressions for the secular perturbations of the orbital elements. The formulae presented should be useful for the reductions of Earth-satellite observations and geopotential studies based on them.List of Symbols semi-major axis - C jk n (, ) cosine functions of and - e eccentricity of the orbit - f acceleration vector of perturbing force - f sin2t - i inclination of the orbit - J n coefficients in the potential expansion - M mean anomaly - n mean motion - p semi-latus rectum of the orbit - R, S, andW components of the perturbing acceleration - r radius-vector of satellite - r magnitude ofr - S jk n (, ) sine functions of and - T time of perigee passage - u argument of latitude - U gravitational potential - true anomaly - V perturbing potential - G(M++m) (gravitational constant times the sum of the masses of Earth and satellite) - n,k coefficients ofR component of disturbing acceleration (funtions off) - n,k coefficients ofS andW components of disturbing acceleration (functions off) - mean anomaly at timet=0 - X 0 n,m zero-order Hansen coefficients - argument of perigee - right ascension of the ascending node  相似文献   

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The empirical evidence for a connection between type and relative angular momentum of galaxies is reviewed and some constraints for the theoretical explanation are discussed.
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