Averaging of the equation of motion of a satellite with respect to its center of mass in degenerate cases: 1. Oscillations in the absolute frame of reference

The problem of attitude oscillations of a satellite with a small dynamic asymmetry in the plane of the orbit leads to a system degenerate to the fifth order from the point of view of the method of averaging. An explicit expression for the dominant term is obtained by integration in the complex plane. The recurrence procedure of calculating the higher approximations of the method of averaging is considered, as well as an approach to the analysis of the structure of derived expressions.     

Orbital stability of planar oscillations of a satellite in a circular orbit

We consider the attitude motion of a satellite with a circular orbit in a central Newtonian gravitational field. The satellite is a solid body whose mass geometry is that of a plate. A nonlinear analysis is made of orbital stability of planar oscillations of the satellite at which its middle or major axis of inertia is perpendicular to the orbit plane. At small amplitudes of oscillations the analysis of stability was made analytically, while for arbitrary amplitudes the numerical analysis was performed.     

卫星在轨抗辐照总剂量数据拟合及其应用

卫星在轨抗辐照总剂量数据是空间电子设备抗辐照校核以及加固设计的依据.用查表法进行抗辐照校核计算时,对于数据表中已有数据点可以精确计算,未知数据点无法精确分析.为进一步提高空间电子设备抗辐照校核计算的精度,同时为辐照特敏感器件选用提供依据,提高产品在轨可靠性.采用分段数据拟合的方法进行了多个型号在轨抗辐照总剂量数据的研究,以中位数为分界点将数据分成前后两部分,前半部分采用分段二次函数拟合,后半部分采用指数函数拟合,拟合精度高,相对误差小于4％,能够满足工程设计的需要.该方法已用于多个在轨型号的抗辐照校核计算,对于提高空间电子设备的可靠性具有积极意义.     

Secular evolution of rotary motion of a charged satellite in a decaying orbit

An electrostatically charged Earth satellite whose orbit is decaying due to the Earths oblateness is considered. Secular perturbations of the orbit are taken into account: they are caused by the second zonal harmonic of the geopotential. These perturbations represent deviations of the longitude of the ascending node and perigee argument, the orbit form being invariable and the orbit inclination to the equatorial plane being constant. The attitude rotary motion of the satellite under the action of perturbing moments of the gravitational and Lorentz forces is studied. The magnetic field of the Earth is taken in a quadrupole approximation. The evolution of the satellites rotary motion is investigated on the basis of new differential equations in s-parameters specially constructed for this purpose. Using the method of averaging, basic regularities of the secular evolution of rotary motion of a screened satellite are revealed. It is found that the rotary motion of a charged satellite essentially depends on the quadrupole component of the geomagnetic potential.__________Translated from Kosmicheskie Issledovaniya, Vol. 43, No. 2, 2005, pp. 111–125.Original Russian Text Copyright © 2005 by Tikhonov.     

Motion of a descent capsule relative to its center of mass when deploying the orbital tether system

The spatial motion relative to the center of mass is considered for a capsule on an elastic tether, when it is unrolled from a spacecraft by a special program. The spacecraft is in a circular orbit and oriented relative to the local vertical, which is guaranteed by operation of its own stabilization system. Angular motion of the capsule relative to the tether direction is studied, and the main factors influencing the stability of this motion are analyzed. An approximate quasi-linear mathematical model of the capsule attitude motion is obtained, which allows one to estimate the influence of major disturbances of its motion. The results of numerical simulations are presented for characteristic cases of the capsule motion.     

Stability and chaos of a damped satellite partially filled with liquid

The stability and chaotic motions of a damped satellite partially filled with liquid which is subjected to external disturbance are investigated in this paper. With linearization analysis, the stability of the two non-trivial equilibrium points is studied. The homoclinic and heteroclinic orbits are found by using the undetermined coefficient method, and the convergence of the series expansions of these two types of orbits is proved. It analytically demonstrates that there exist homoclinic orbits of the Si’lnikov type that join the two non-trivial equilibrium points to themselves, and therefore smale horseshoes and the horseshoe chaos occur for this system via the Si’lnikov criterion. In addition, there also exists a heteroclinic orbit connecting the two non-trivial equilibrium points. Numerical simulations are also given, which verify the analytical results. The system can be chaotic through period-doubling bifurcations as the amplitude of the external disturbance varies, and backward period-doubling bifurcations as the angular momentum of the rotor varies.     

Effects of eccentricity of the reference orbit on multi-tethered satellite formations

The paper discusses the relevance of eccentric reference orbits on the dynamics of a tethered formation, when a massive cable model is included in the analysis of a multi-tethered satellite formation. The formations examined in this study are hub-and-spoke (HAS) and closed-hub-and-spoke (CHAS) configurations for in-plane and Earth-facing spin planes. Stability of the formations is studied by means of numerical simulation, together with the evaluation of the effects of eccentricity on tether elongation, agents relative position, and formation orientation and shape.     

Body orientation and center of mass control in microgravity

The control of the body orientation and the center of mass position with respect to the feet was investigated under normo- and microgravity (space flight Altair), during erect posture and at the end of a forward or backward upper trunk movement.

It was observed that during erect posture, the trunk orientation with respect to the vertical was inclined some 6 ° forward in both subjects under microgravity, whereas it was vertical or slightly backward oriented under normogravity. Under microgravity, on the contrary, the initial position CM changed either backwards or forwards. This result suggests that the inclined trunk posture might be due to misevaluating the vertically under microgravity and that different control mechanisms are involved in orienting the trunk and placing the CM.

It was also noted that the final position of the CM at the end of the movement did not differ markedly between microgravity and normogravity. This result suggests that the kinematic synergies which stabilize the CM during uppertrunk movements may result from an automatic central control which is independent from the gravity constraints.     

The motion of a synchronous satellite in a system similar to the earth-moon system

The stationary motions of a synchronous axisymmetric satellite are studied in the field of attraction by the Earth and a third body whose parameters are close to those of the Moon. Equations of motion are written in canonical variables that take into account the resonance character of the problem. The plots characterizing the dependence of the rotation parameters of the satellite relative to the center of mass on the elements of satellite’s translational motion are presented. A picture is given that represents the initial configuration of the system for implementing stationary motions.     

On the one-body problem in the field of a tall cylinder in orbit

We describe the motion of a material point that is attracted by a tall, homogeneous cylinder. The cylinder moves on a circular orbit and points in the radial direction. The finite solution can be expanded in powers of two small parameters: the initial eccentricity of the orbital motion about the cylinder and the coupling parameter of the Coriolis force. Such expansions are given for the case of the indifferent longitudinal location. Solutions periodic in the polar angle are constructed. We do not find resonance effects or other large cumulative amplitude variations that might be due to the gravity-gradient and Coriolis force.     

Optimization of passive orbit with the use of gravity maneuver

A high-precision method of calculating gravitational interactions is applied in order to determine optimal trajectories. A number of problems, necessary for determination of optimal parameters at a launch of a spacecraft and during its flyby near celestial bodies, are considered. The spacecraft trajectory was determined by numerical integration of the equations of passive motion of the spacecraft and of the equations of motion for planets, the Sun, and the Moon. The optimal trajectory of the spacecraft approaching the Sun is determined by fitting its initial conditions.     

微纳卫星发展现状及在光学成像侦察中的应用

对当前微纳卫星在空间环境感知、新技术空间演示验证、空间科学试验、通信与数据传输、对地或对空间目标进行光学成像观测等方面的主要应用形态进行了归纳总结,分析了采用微纳卫星实施光学成像侦察的优势,给出了应用实例,并提出在航天侦察应用中大力发展光学成像侦察微纳卫星的相关建议。从而为后续微纳卫星在航天光电侦察中的广泛应用提供了参考。     

Modal control of the planar motion of a long flexible beam in orbit

Attitude control techniques for the pointing and stabilization of very large, inherently flexible spacecraft systems are investigated. The attitude dynamics and control of a long, homogeneous flexible beam whose center of mass is assumed to follow a circular orbit is analyzed. In this study, first order effects of gravity-gradient are included, whereas external perturbations and related orbital station keeping maneuvers are neglected. A mathematical model which describes the system deflections within the orbital plane has been developed by treating the beam as having a maximum of three discretized mass particles connected by massless, elastic structural elements. The uncontrolled dynamics of this system are simulated and, in addition, the effects of the control devices are considered. The concept of distributed modal control, which provides a means for controlling a system mode independently of all other modes, is examined. The effect of varying the number of modes in the model as well as the number and location of the control devices are also considered.     

Equilibrium positions of a weight on a cable fixed to a dumbbell-shaped space station moving along a circular geocentric orbit

The motion of a space object in the gravitational field of the Earth is considered. The object consists of an extended space station and a weight, which is free to move along the cable fixed to the ends of the station. It is assumed that the station is composed of two masses coupled by a weightless rod, while the cable is weightless and non-stretched. The equations of motion of such a system are derived for the case when the motion proceeds in a single plane, while the center of mass of the system moves along a circular geocentric orbit. The conditions of the cable tension (conditions of being on tie) are derived. The phase portrait of the weight motion along the cable is constructed when the station is oriented to the attracting center or is perpendicular to this position. The possibility to leave the tie in this case is analyzed. Equilibrium configurations of the system are found, i.e., such motions of the object under consideration at which the weight does not change its position relative to the station. Lyapunov stability of such configurations is analyzed for two situations: when the station is composed of equal masses and when masses at the ends of the station are different. In particular, for the case of different masses it is established that there exist such positions of equilibrium at which the dumbbell is located at an angle to the direction to the attracting center. In some cases these positions can be stabilized (if the weight is fixed on the cable).     

From Earth's orbit to the outer planets and beyond: Psychological issues in space

Current planning for the first interplanetary expedition to Mars envisions a crew of 6 or 7 people and a mission duration of around 2.5 years. However, this time frame is much less than that expected on expeditions to the outer solar system, where total mission durations of 10 years or more are likely. Although future technological breakthroughs in propulsion systems and space vehicle construction may speed up transit times, for now we must realistically consider the psychological impact of missions lasting for one or more decades.Available information largely deals with on-orbit missions. In research that involved Mir and ISS missions lasting up to 7 months, our group and others have studied the effects of psychological and interpersonal issues on crewmembers and on the crew-ground relationship. We also studied the positive effects of being in space. However, human expeditions to the outer planets and beyond will introduce a number of new psychological and interpersonal stressors that have not been experienced before. There will be unprecedented levels of isolation and monotony, real-time communication with the Earth will not be possible, the crew will have to work autonomously, there will be great dependence on computers and other technical resources located on board, and the Earth will become an insignificant dot in space or will even disappear from view entirely.Strategies for dealing with psychological issues involving missions to the outer solar system and beyond will be considered and discussed, including those related to new technologies being considered for interstellar missions, such as traveling at a significant fraction of the speed of light, putting crewmembers in suspended animation, or creating giant self-contained generation ships of colonists who will not return to Earth.     

Longitude-dependent effects of fragmentation events in the geosynchronous orbit regime

The effects of on-orbit fragmentation events on localized debris congestion in each of the longitude slots of the geosynchronous orbit (GEO) regime are evaluated by simulating explosions and collisions of uncontrolled rocket bodies in multiple orbit configurations, including libration about one or both of the gravitational wells located at 75°E and 105°W. Fragmentation distributions are generated with the NASA Standard Breakup Model, which samples fragment area-to-mass ratio and delta-velocity as a function of effective diameter. Simulation results indicate that the long-term severity and consequence of a GEO fragmentation event is strongly dependent upon parent body longitude at the epoch of fragmentation, which can spawn bi-annual “fragment storms” in high-risk longitude slots, driven by lower-energy fragments that have been captured and have started librating around the nearby gravitational well.     

Rapid rotations of a satellite with a cavity filled with viscous fluid under the action of moments of gravity and light pressure forces

Rapid rotational motion of a dynamically asymmetric satellite relative to the center of mass is studied. The satellite has a cavity filled with viscous fluid at low Reynolds numbers, and it moves under the action of moments of gravity and light pressure forces. Orbital motions with an arbitrary eccentricity are supposed to be specified. The system, obtained after averaging over the Euler-Poinsot motion and applying the modified averaging method, is analyzed. The numerical analysis in the general case is performed, and the analytical study in the axial rotation vicinity is carried out. The motion in the specific case of a dynamically symmetric satellite is considered.     

Periodic motions of a nearly dynamically symmetric satellite in the neighborhood of hyperboloidal precession

The motion of a satellite close to a dynamically symmetric solid body in a Newtonian gravitational field over a circular orbit is studied. The system of differential equations describing the body’s motion is close to a system with cyclic coordinate. New classes of periodic motions are constructed in the neighborhood of a known partial solution to an unperturbed problem, hyperboloidal precession of a dynamically symmetric satellite. In the resonance case, when the ratio of one frequency of small oscillations of a reduced system with two degrees of freedom in the neighborhood of a stable equilibrium position to the frequency of cyclic coordinate variation is close to an integer number, there exist one or three families of periodic motions that are analytic in terms of fractional powers of a small parameter. A study of stability of these motions was performed with the help of KAM (Kolmogorov-Arnold-Moser) theoty. Faling the described resonance there exists a unique family of periodic motions that is analytic in terms of integer powers of a small parameter. The check-up of stability of these motrons was carried out. We distinguished the cases of parametric resonance, resonances of the third and fourth orders, and a non-resonant case. In the resonance cases our study relies on well-known results on stability of Hamiltonian systems during resonances [1]. In the non-resonant case we use the KAM theory [2].