Dynamics of a plasma ring rotating in the magnetic field of a central body: Magneto-gravitational waves

The model problem of the dynamics of a planar plasma ring rotating in the dipole magnetic field of a central body is considered. A finite-dimensional mathematical model of the system is synthesized by the Boubnov-Galerkin method. The class of solutions corresponding to magneto-gravitational waves associated with deformations of the ring boundaries is investigated.     

Adiabatic invariants of the solar system and exo-planet systems and soliton-like disturbances of Alfvenic plasma proto-ring

Some new results are presented concerning quantization of observed parameters of the Solar System and exo-planet systems, as well as some functions of these parameters. General adiabatic invariants are introduced including (for the Solar System) orbital quantum numbers of planets and quantum numbers characterizing their proper rotation (spin). The quantization of parameters relating to satellite and exo-planetary systems is considered. Some arguments are presented about the influence of nonlinear disturbances of Alfvenic plasma proto-ring of the type of Frenkel-Kontorova (FK) and Russell-Korteweg-de Vries (KdV) solitons on formation of elite rings and their evolution with conservation of corresponding invariants. A mechanical model is synthesized that describes nonlinear FK soliton type disturbances of magnetized plasma.     

On stability of a rotating spacecraft partially filled with liquid: The case of a single cavity

The problem of stability of a rotating spacecraft with a cavity partially filled with liquid to a small depth is considered with regard to the distinction in angular velocities of spacecraft and liquid rotation and their variability (the modes of the spacecraft’s stationary rotation, spin-up, and rotation deceleration). The regions of stability (in space of the characteristic parameters of an object) are found, and mathematical simulating of the disturbed motion is carried out.     

基于惯性系的双轴旋转式惯导系统转位方法

针对双轴旋转式惯导系统中不能自动补偿标度因数误差与地球自转耦合误差的问题,提出了一种改进的转位方法。该方法不增加转轴数目,通过补偿地球自转在转轴平面的投影抑制耦合误差项,计算结果表明该方法适用于激光陀螺惯导系统和光纤陀螺惯导系统。利用改进的转位方法对双轴旋转式惯导系统进行仿真,仿真结果验证了该方法的可行性。研究结果为双轴旋转式惯导系统的工程设计和改进提供了一定的理论支持。     

Application of a magnetohydrodynamic element in the control loop of a rotating spacecraft with a spike antenna

The problem of stabilization of a rotating spacecraft with a flexible spike antenna located along the axis of spacecraft rotation is considered. A magnetohydrodynamic element is used as a final-control element in the control loop of spacecraft attitude, and the solar direction sensor serves as a measuring device. At the first stage of investigation, the problem of stability is considered for stationary and non-stationary modes of rotation of the spacecraft with a flexible antenna and with a cavity partially filled with a low-viscosity liquid.     

Stability of a ring of connected satellites

The motion of a large number of artificial satellites connected in a ring one after another by tethers of variable length is considered. Every satellite is supposed to have a control system programmed according to some tether tension law as a function of the distance between tethered satellites. The effect of the tension control law on the stability of stationary rotation of this ring is investigated. The final stability condition includes two requirements: 1) the nominal tether tension should be less than a definite limit equal, up to numerical coefficient, to one satellite weight divided by the number of satellites; 2) tether tension should decrease (or remain constant) with the increase of the distance between tethered satellites. In dynamics the artificial rings of this kind are much like their natural prototype—meteor rings. On the other hand, the investigation of the artificial rings contributes to developing an unexpected view upon meteor rings, suggesting a model of an imaginary equivalent string.     

Stabilization of a Reentry Vehicle by a Partial Spin-up during Uncontrolled Descent

Stabilization of a reentry vehicle (RV) by a partial spin-up of it is considered for the case of uncontrolled descent into the atmosphere. In this case, the vehicle is a composite construction consisting of two rigid bodies, a return capsule and a stabilizing block, which is put in rotation. A model is developed for the spatial motion of the reentry vehicle considered as a system of coaxial rigid bodies rotating about a common axis of symmetry. The free motion is studied, and the stability of steady-state regimes is analyzed. The spatial motion of the system is considered for the case of a small asymmetry due to displacement of the axes of dynamic symmetry of the bodies with respect to the spin axis, and approximate solutions for the motion parameters of the free system are found.     

Evolution of motion of two viscoelastic planets in the field of forces of their mutual attraction

Translational-rotational motion of two viscoelastic planets in a gravitational force field is studied. The planets are modeled by homogeneous isotropic viscoelastic bodies. In their natural undeformed state each of the planets represents a sphere. We investigate a specific case when the planet’s centers of mass move in a fixed plane, the axis of rotation for each planet being directed along the normal to this plane. An equation describing the evolution of a slow angular variable (perihelion longitude) is derived. The observed displacement of the perihelion of Mercury is compared with the results obtained in the considered model problem about motion of two viscoelastic planets. Quite important is the fact that the planet of smaller mass (Mercury) moves not in a central Newtonian field of forces, but rather in the gravitational field of a rotating viscoelastic planet (Sun).     

Stationary Motions of a Homogeneous Meteor Ring in the Gravitational Field of a Center

The problem of studying a ring in the gravitational field of a center arose after the discovery of Saturn's rings by Galileo and subsequent discovery of the rings of other planets of the Solar System. Modern theoretical investigations of the existence and stability of planetary rings are mostly related to studies of plane differentially rotating discs [1]. As opposed to this line of research, this paper follows the approach established in classical works [2–4].     

Convection of liquid with internal heat release in a rotating container

The convection of heat-generating fluid in a rotating horizontal cylinder is experimentally investigated. The threshold of convection excitation, the structure of convective flows and the heat transfer in the cylinder depending on the heat release capacity, liquid viscosity and aspect ratio of the cavity are studied. It is found that the average convection is excited by the thermovibrational mechanism —the gravity force, rotating in the cavity frame, produces the oscillations of non-isothermal fluid relative to the wall, which in turn result in excitation of mean convective flows. It is shown that the structure of convective flows depends on the dimensionless velocity of rotation. At relatively low rotation velocity the convection develops in the form of a periodic system of vortices regularly distributed along the cylinder axis. The threshold of excitation (critical value of vibration parameter) of three-dimensional vortex structures grows with rotation velocity. Above some definite rotation velocity the convection develops as two-dimensional rolls parallel to the axis of rotation. The threshold of two-dimensional structures excitation does not depend on the rotation velocity. Besides the structure of thermal convective flows the analysis of the relatively weak currents generated by the inertial waves below the threshold of convection is performed.     

Effect of parametric and nonlinear perturbations on statistical dynamics of the Earth’s pole

We study the influence of additive and parametric slowly varying harmonic (at the Chandler frequency and doubled frequency) and stochastic Gaussian broadband perturbations on mathematical expectations, variances, and covariations of oscillations of the Earth’s pole. The influence of perturbations on both regular and irregular stochastic oscillations is considered in detail. Results of numerical experiments are presented. The developed models and software are included into information resources on the fundamental problem “Statistical dynamics of the Earth’s rotation” of Russian Academy of Sciences.     

Multipole Models of the Earth's Magnetic Field

To develop a mathematical model of rotational motion of an artificial satellite about its center of mass under the action of various forces (magnetic, Lorentz, etc.) caused by the geomagnetic field, it is necessary to know the induction of the Earth's magnetic field (EMF) as a function of the radius vector of a given point in the near-Earth space. Because the EMF possesses a complex structure and the above-mentioned functional dependence is unavailable in explicit analytic form, a set of approximate models of the EMF should be used. The simplest such model—a right dipole (aligned with the axis of rotation)—does not enable one to reveal in detail the influence of diurnal EMF rotation on the rotational motion of a satellite. The next EMF approximation—an inclined magnetic dipole—does not suffer from the above-mentioned drawback. However, it is shown that not all corrections to the magnetic induction of the EMF of the same order of magnitude are taken into account in the course of transformation from the model of aligned dipole to the model of inclined dipole. So, to develop the EMF model accurately accounting for the absence of axial symmetry of the EMF with respect to the axis of diurnal rotation of the Earth, in general, the effect of the quadrupole component of the geomagnetic potential on the EMF induction (and, probably, even the components of higher orders) must be taken into consideration. By using the International Geomagnetic Reference Field IGRF-2000, the multipole models of the EMF, corresponding to quadrupole, octupole, and higher-order approximations, were constructed and studied in this work. The EMF potential is expressed in terms of its multipole tensors. As a result, projections of the induction and induction gradient of EMF in the center of mass of the satellite onto the axes of the orbital coordinate system can be written in convenient and concise form. The expressions for the first four multipole tensors through the known geomagnetic constants are found. A method for estimating the reliability of these models is put forward, and the regions of applicability of the quadrupole and octupole models are drawn on the plane of orbital parameters.     

The role of motor processes in mental rotation: selective shaping of cognitive processing via specific sensorimotor experience

The involvement of motor processes in mental rotation is experience-dependent: different levels of expertise in sensorimotor interactions lead to different strategies in mental rotation. In the present study, wrestlers, gymnasts, and nonathletes physically rotated objects that were either light (wooden) or heavy (lead) but otherwise having the same sizes and shapes. They then performed a mental rotation task using photographs of these objects in which the material and therefore the weight was visible. I hypothesized that wrestlers would rely more heavily on experience-based sensorimotor strategies in performing mental rotation because during their athletic practice they not only manipulate external “objects” (i.e., their opponent) but also have to plan future actions taking into account past experience of these “objects” (for example their weight). All participants reported that lead objects were harder to physically rotate than wooden ones. However, only wrestlers mentally rotated lead objects more slowly than wooden ones—as they would if they were physically rotating them—suggesting the involvement of motor processes. These findings show that the involvement of motor processes in mental rotation depends on specific rather than mere sensorimotor experience.     

Refinement of the Oblique Dipole Model in the Evolution of Rotary Motion of a Charged Body in the Geomagnetic Field

When solving problems related to the induction of the Earth's magnetic field, the potential of which is expressed in the form of a series of spherical harmonic functions, it is necessary to use an approximate model of the geomagnetic field that satisfies the two conflicting requirements of simplicity and accuracy. As is noted in [3, p. 10], at the stage of design of satellites, especially at the stage of preliminary analysis of their dynamics, simple models of the geomagnetic field are usually employed. This offers additional possibilities for theoretical analysis of the problem. The averaged model and the model of a right dipole are just such simple models. The quadrupole model of the geomagnetic field developed in [4] is more accurate, but also more complex. The model of an oblique or skewed dipole is intermediate. The quadrupole model generalizes the simpler models mentioned above, and its analysis allows estimation of the accuracy of each model. It turns out that the oblique dipole model, which differs from the model of a right dipole by small correcting terms, does not take into account other correcting terms caused by the quadrupole part of the geomagnetic field, which are greater in magnitude. The evolution of the rotary motion of a charged rigid body in the geomagnetic field is considered, and the incorrectness of the oblique dipole model is demonstrated. The effect of the quadrupole component of the geomagnetic field on the body dynamics is revealed.     

A Celestial Mechanics Model of Oscillations of the Poles of a Deformable Earth

The problem of Chandler motion of the Earth's poles is studied in the context of the model of a viscoelastic body. The Earth-Moon system is considered as a binary planet rotating around their barycenter. Numerical values of the period and amplitudes of oscillations of the poles are obtained by estimating the elastic deformation of the Earth and the variation of its inertia tensor, and they agree well with observational data. An evolution model of the Earth-Moon-Sun system is constructed by taking into account tidal forces of dissipation character. By means of the method of averaging, the qualitative properties of motion on asymptotically large intervals of time (comparable and essentially longer than the period of precession of the Earth's axis) are established and commented on.     

Navigating in a Virtual 3D Maze: Body and Gravity,Two Possible Reference Frames for Perceiving and Memorizing

Although recent studies have brought new insight into the mechanisms of spatial memory and cognitive strategies during navigation, most of these studies have concerned two-dimensional navigation and little is known regarding the problem of three-dimensional (3D) spatial memory. We found previously that memorizing complex 3D-structured corridors was easier with natural self-motion that included only yaw turns, and vertical translations facing the walls at vertical sections. This suggests that when only sideways (yaw) mental rotations had to be performed in order to shift from the experienced egocentric to the allocentric reference frame where recognition was tested, memorization of such corridors was improved. In the present investigation we studied the effect of tilting separately subject's body axis and self-motion's rotation axis relative to gravity. With a computerized 3D reconstruction task of the maze, we examined whether having any single rotation axis was enough to facilitate this reference shift or, if not, what aspect of the terrestrial condition-where visual displacement rotation, gravity and body axes were aligned-led to better performance. Field dependent (FD) and independent (FI) subjects, as determined by the rod and frame test, showed distinct effects of the navigation conditions. The FD group performance was markedly impaired when gravity and body axis were in conflict, independently of the rotation axis, whereas FI performance only slightly worsened when the body was tilted and the rotation axis remained aligned with gravity. Moreover, tilting the body in the control condition only worsened performance for the FD group.     

Asymptotic study of a complete magnetic attitude control cycle providing a single-axis orientation

The angular motion of an axisymmetrical satellite equipped with the active magnetic attitude control system is examined. Attitude control system has to ensure necessary orientation of the axis of symmetry in the inertial space. It implements the following strategy: coarse reorientation of the axis of symmetry with nutation damping or “-Bdot” without initial detumbling; spinning-up about the axis of symmetry to achieve the property of a gyro; fine reorientation of the axis in the inertial space. Dynamics of the satellite is analytically studied using averaging technique on the complete control loop consisting of five algorithms. Solutions of the equations of motion are obtained in terms of quadratures for most cases or even in closed-form. The latter allowed to study the dependence of motion parameters including time-response with respect to the orbit inclination and other parameters for all algorithms.     

The Use of Quaternions in the Optimal Control Problems of Motion of the Center of Mass of a Spacecraft in a Newtonian Gravitational Field: III

The results of numerical solution of the problem of a rendezvous in the central Newtonian gravitational field of a controlled spacecraft with an uncontrollable spacecraft moving along an elliptic Keplerian orbit are presented. Two variants of the equations of motion for the spacecraft center of mass are used, written in rotating coordinate systems and using quaternion variables to describe the orientations of these coordinate systems. The problem of a rendezvous of two spacecraft is formulated [1, 2] as a problem of optimal control by the motion of the center of mass of a controlled spacecraft with a movable right end of the trajectory, and it is solved on the basis of Pontryagin's maximum principle. The paper is a continuation of papers [1, 2], where the problem of a rendezvous of two spacecraft has been considered theoretically using the two above variants of the equations of motion for the center of mass of the controlled spacecraft.     

A study of evolution of spin-up mode of a satellite in the plane of its orbit

We investigate the mode of spinning up a low-orbit satellite in the plane of its orbit. In this mode the satellite rotates around its principal central axis of the minimum moment of inertia which executes small oscillations with respect to the normal to the orbit plane; the angular velocity of the rotation around this axis several times exceeds the mean orbital motion. Gravitational and restoring aerodynamic moments are taken into account in the satellite’s equations of motion. A small parameter characterizing deviation of the satellite from a dynamically symmetric shape is introduced into the equations. A two-dimensional integral surface of the equations of motion, describing quasi-steady-state rotations of the satellite close to cylindrical precession of the corresponding symmetrical satellite in a gravitational field, has been studied by the method of small parameter and numerically. Such quasi-steady-state rotations are suggested to be considered as unperturbed motions of the satellite in the spin-up mode. Investigation of the integral surface is reduced to numerical solution of a periodic boundary value problem of a certain auxiliary system of differential equations and to calculation of quasi-steady-state rotations by the two-cycle method. A possibility is demonstrated to construct quasi-steady rotations by way of minimization of a special quadratic functional.