Evolution of the satellite fast rotation due to the gravitational torque in a dragging medium (original) (raw)
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Resonance in the motion of a geocentric satellite due to Poynting-Robertson drag
2017
This paper focuses on resonance of the motion of a geocentric synchronous satellite under the effect of gravitational forces of the Sun-Earth system subject to Poynting Robertson (PR) drag. With the assumption that the two bodies (the Earth, the Sun) lie in an ecliptic plane and the third body (satellite) lie in the orbital plane, five resonance points results from commensurability between the average angular velocity of the Earth and the mean motion of satellite. The amplitude and time period of the oscillation have been determined here in different cases at the resonance points.
Analytic theory of orbit contraction due to atmospheric drag
Acta Astronautica, 1979
Theory of space vehicle flight in near vacuum and in a planetary atmosphere is unified for the case of a spherically symmetric atmosphere with exponential variation of density with height. Dimensionless equations of motion are established that bridge the gap between satellite theory and entry theory. Integration is done by Poincare's method of perturbations. Solutions for the dimensionless semimajor axis are numerically obtained.
Resonance in Satellite’s Motion Under Air Drag
American Journal of Applied Sciences, 2006
This article studies the attitude motion of a satellite in a circular orbit under the influence of central body of mass M and its moon of mass m, whose orbit is assumed to be circular and coplanar with the orbit of the satellite. The body is assumed to be tri-axial body with principal moments of inertia A < B < C at its centre of mass, C is the moment of inertia about the spin axis which is perpendicular to the orbital plane. These principal axes are taken as the coordinate axes x, y, z; the z axis being perpendicular to the orbital plane. We have studied the rotational motion of satellite in the circular orbit under the influence of aerodynamic torque. Using BKM method, it is observed that the amplitude of the oscillation remains constant upto the second order of approximation. The main and the parametric resonance have been shown to exist and have been studied by BKM method. The analysis regarding the stability of the stationary planar oscillation of a satellite near the resonance frequency shows that the discontinuity occurs in the amplitude of the oscillation at a frequency of the external periodic force which is less than the frequency of the natural oscillation.
Resonance in the Motion of Geocentric Satellites due to Poynting-Robertson Drag
International Journal of Vehicle Structures and Systems, 2018
The problem of resonance in a geocentric synchronous satellite under the gravitational forces of the Sun and the Earth subject to Poynting-Robertson (P-R) drag is the subject matter of this paper. Based on the assumption that the two bodies the Earth and the Sun lie in ecliptic plane and the satellite in the orbital plane. Five resonance points results from commensurability between the mean motion of the satellite and the average angular velocity of the Earth. Out of all resonance, the 3:2 and 1:2 resonance occurs only due to velocity dependent terms of P-R drag. We have determined the amplitude and time period of the oscillation in two different cases at those resonance points.
Aerodynamic Torque exhibits non –resonance oscillation in satellite motion
Mathematica Applicanda, 2017
This paper deals with the non-linear oscillation of a satellite in an elliptic orbit around the Earth under the inuence of aerodynamic and gravitational torque. It is assumed that the orbital plane coincides with the equatorial plane of the Earth. Using BogoliubovKrylovMitropolsky (BKM) methods of nonlinear oscillations, it is observed that the amplitude of the oscillation remains constant up to the second order of approximation. Numerically time series, 2D and 3D phase spaces are plotted for Earth Moon system using Matlab. The existence of main and parametric resonance concludes the dierent frequency states which transit the motion from regular to an attractor that leads to chaotic state.
On the stability of spinning satellites
Acta Astronautica, 2011
We study the directional stability of rigid and deformable spinning satellites in terms of two attitude angles. The linearized attitude motion of a free system about an assumed uniform-spin reference solution leads to a generic MGK system when the satellite is rigid or deformable. In terms of Lyapunov's stability theory, we investigate the stability with respect to a subset of the variables. For a rigid body, the MGK system is 6-dimensional, i.e., 3 rotational and 3 translational variables. When flexible parts are present the system can have any arbitrary dimension. The 2 Â 2 McIntyre-Myiagi stability matrix gives sufficient conditions for the attitude stability. A further development of this method has led to the Equivalent Rigid Body method. We propose an alternative practical method to establish sufficiency conditions for directional stability by using the Frobenius-Schur reduction formula. As practical applications we discuss a spinning satellite augmented with a spring-mass system and a rigid body appended with two cables and tip masses. In practice, the attitude stability must also be investigated when the spinning satellite is subject to a constant axial thrust. The generic format becomes MGKN as the thrust is a follower force. For a perfectly aligned thrust along the spin axis, Lyapunov's indirect method remains valid also when deformable parts are present. We illustrate this case with an apogee motor burn in the presence of slag. When the thrust is not on the spin axis or not pointing parallel to the spin axis, the uniform-spin reference motion does not exist and none of the previous methods is applicable. In this case, the linearization may be performed about the initial state. Even when the linearized system has bounded solutions, the non-linear system can be unstable in general. We illustrate this situation by an instability that actually happened in-flight during a station-keeping maneuver of ESA's GEOS-I satellite in 1979.
Behavior of nearby synchronous rotations of a Poincaré–Hough satellite at low eccentricity
Celestial Mechanics and Dynamical Astronomy, 2012
This paper presents a study of the Poincaré-Hough model of rotation of the synchronous natural satellites, in which these bodies are assumed to be composed of a rigid mantle and a triaxial cavity filled with inviscid fluid of constant uniform density and vorticity. In considering an Io-like body on a low eccentricity orbit, we describe the different possible behaviors of the system, depending on the size, polar flattening and shape of the core. We use for that the numerical tool. We propagate numerically the Hamilton equations of the systems, before expressing the resulting variables under a quasi-periodic representation. This expression is obtained numerically by frequency analysis. This allows us to characterise the equilibria of the system, and to distinguish the causes of their time variations. We show that, even without orbital eccentricity, the system can have complex behaviors, in particular when the core is highly flattened. In such a case, the polar motion is forced by several degrees and longitudinal librations appear. This is due to splitting of the equilibrium position of the polar motion. We also get a shift of the obliquity when the polar flattening of the core is small.
A Third-Order Theory for the Effect of Drag on Earth Satellite Orbits
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 1992
Analytical theory for the motion of near-Earth satellite orbits with the air drag effect is developed in terms of the KS elements, utilizing an analytical oblate exponential atmospheric model. The series expansions include up to cubic terms in e (eccentricity) and c (a small parameter dependent on the flattening of the atmosphere). Due to the symmetry of the KS element equations, only one of the eight equations is integrated analytically to obtain the state vector at the end of each revolution. Numerical comparisons are made with nine test cases, selected to cover a wide range of eccentricity with perigee heights near to 300 km at three different inclinations. A comparison of three orbital parameters: semi-major axis, eccentricity and argument of perigee, perturbed by air drag with oblate atmosphere is made with the previously developed second-order theory. It is found that with the present theory with increase in eccentricity there is improvement in semi-major axis and eccentricity...
Mechanics of Solids, 2016
We study the fast rotational motion of a dynamically asymmetric satellite with a spherical cavity filled with a highly viscous liquid about the center of mass under the action of gravitational torque and medium drag torques. The system obtained by averaging over the Euler-Poinsot motion and by using a modified averaging method is analyzed. An analytic study and numerical analysis are carried out.
Orbital effects of the Magnus force on a spinning spherical satellite in a rarefied atmosphere
European Journal of Mechanics B-fluids, 2008
The effects of the Magnus force on a spinning sphere in a Keplerian orbit is investigated using perturbation theory. The result is that the plane of the orbit will rotate with the angular velocity − 1 4 α τ mn ρ S ω, where α τ is the accommodation coefficient of tangential momentum, m and n are the mass and number density of the surrounding gas, and where ρ S and ω are the mean density and the angular velocity of the sphere. It is shown that under reasonable assumptions, for a spinning satellite in the Earth's atmosphere, this effect is small.