Alexandr Zakrzhevskii - Academia.edu (original) (raw)

Papers by Alexandr Zakrzhevskii

ABSTRACT The cable-suspension method is used to simulate weightlessness on Earth in the general c... more ABSTRACT The cable-suspension method is used to simulate weightlessness on Earth in the general case. By an example of mathematical simulation of a system of rigid bodies connected via hinged joints and suspended from a special facility, it is shown that the method developed provides realistic simulation of orbital processes under earth conditions. The validation criterion for the simulation is the closeness of the values of the forces and moments in joints and the attitude and angular velocities to their theoretical values in orbital motion

International Applied Mechanics, 1999

The authors consider the problem of deployment in orbit of a small tether that can serve as a sta... more The authors consider the problem of deployment in orbit of a small tether that can serve as a standard of length fiw calibration of both onboard and ground optical and radar tracking systems, as an integrated sensor of the force fields of planets, etc. A tether for two bodies is examined. Possible methods for compact placement of a tether in orbit in operating condition are discussed. The main method is that of use of the centrifugal fi~rces resulting from imparting to the tether an initial angular velocity in its deployment from the spacecraft. Various methods for creating moments of friction forces in hinges are considered. Numerical modeling of the dynamic processes is carried out within the framework of the theory of systems of bodies. Problems associated with determination of the required initial angular velocity and of the "cone of departure" of the tether from the spacecraft are examined.

International Applied Mechanics, 2004

The dynamics of a system of rigid bodies with program-variable configuration is analyzed. A mathe... more The dynamics of a system of rigid bodies with program-variable configuration is analyzed. A mathematical model is constructed using methods of analytical mechanics. The behavior of a microsatellite with a deployable gravity-gradient boom is analyzed as a numerical example

International Applied Mechanics, 2007

The equilibrium states of an electrodynamic tether between two bodies of small mass in a near-pol... more The equilibrium states of an electrodynamic tether between two bodies of small mass in a near-polar orbit are studied. The behavior of the following parameters is traced during an astronomical day: tension of the tether, its radius of curvature, the angle of deviation from the orbital plane, induced electrodynamic force, etc. The lifetime of the tether in a circular near-earth orbit is analyzed

International Applied Mechanics, 2006

The object to be studied is a spacecraft with a deployable pantograph structure as a solar-batter... more The object to be studied is a spacecraft with a deployable pantograph structure as a solar-battery carrier. The objective of research is to design a mathematical model of this structure taking the elasticity of pantograph elements into account. The Lagrangian formalism is followed. To model the dynamic processes in the system, a software package has been developed, which can be adapted, if necessary, to study deployable structures of other types. The behavior of the structure during deployment, collapse, and redeployment under the action of various perturbations is modeled numerically. Plots illustrating the variation of characteristic variables are presented

Journal of Modeling, Simulation, Identification, and Control, 2014

The present paper deals with the study of the dynamics of a spacecraft with a gravitational syste... more The present paper deals with the study of the dynamics of a spacecraft with a gravitational system of stabilization, with a magnetic damper, and pitch flywheel. Primarily the boom of the gravitational stabilizer is a prestressed tape wound on a special drum. When the drum starts deploying the tape, its takes the shape of an elastic long boom with the mass on its tip. The objective of the study is the mechanical and mathematical modeling and numerical simulation of the spacecraft dynamics. The equations of motion are derived with the use of the Eulerian-Lagrangian formalism. The information, which is obtained by a numerical simulation, gives the conclusion that the deployment and functioning of the spacecraft can be used to design a rational choice of parameters of the spacecraft. The data obtained allow choosing of the most suitable law of deployment and parameters of the magnetic damper. A detailed simulation has allowed analyzing the dynamic behavior of the design at various values of parameters of the spacecraft with the gravitational stabilizer. Data obtained facilitate selection the most appropriate deployment, structure and damper parameters.

Acta Astronautica, 2009

The present paper deals with the study the dynamics of the spacecraft with gyro-gravitational sys... more The present paper deals with the study the dynamics of the spacecraft with gyro-gravitational system of stabilization. The deployment of the boom of the gravitational stabilizer commences after placing the spacecraft into the orbit and completion of the preliminary damping, when the gyroscopes are uncaged. Primarily the boom is the pre-stressed tape wound on the special drum. When the drum starts deploying the tape, it turns into the elastic cylindrical rod with the mass at its tip. The objective of the study is the creation of the generalized mathematical model and the conducting of the computer modelling of the spacecraft dynamics. The equations of motion are worked out with the use of the Lagrangian formalism. The numerical simulation of typical modes of system functioning is conducted. It is shown that the folding and the following deployment of the boom result in the turn of the spacecraft by 180 • about the axis of the pitch. The results illustrate the behaviour of the main system variables.

Int Appl Mech Engl Tr, 1979

A great deal of interest has been shown lately in producing programmed motion in space which invo... more A great deal of interest has been shown lately in producing programmed motion in space which involves Controllable bodies in a central force field. In several studied such as [3], e.g., there have been constructed adaptive laws of control which will ensure stable execution of programmed motion by a solid body carrying three single-stage gyros. In this study the problem will be solved for the case of a solid carrier to which elastic elements have been attached. We consider a body having a large mass m, shown in Fig. i. This body contains elastic elements and a rigid part. The presence of elastic elements substantially alters the properties of an object which is not a gyrostat. It is not possible, in the general case, to define its state by a finite number of parameters. Therefore, the set of measuring instruments aboard the carrier is becoming morecomplex. Let the body carry orientation angle and angular velocity transducers, torque transducers sensing the moments exerted on the carrier by the elastic elements, also linear accelerometers, aontrol torque generators, servomechanism components. As servomechanism components will be used three single-stage gyros with their axes oriented along the principal axes of intertia of the system in the undeformed state. On the diagrams in Figs. 1 and 2 we have the following systems of coordinates: inertial C,XIX2X~, orbital Cxlx2xs, principal central axes of the undeformed Ox~x2x3, translationally moving axes 0~2~s, and axes Cx,Cx2Cx3 c parallel to axes Ox,x2x3 and with the origin C of coordinates at the instantaneous center of mass of the system in the deformed state.

Int Appl Mech Engl Tr, 1980

Int Appl Mech Engl Tr, 1973

lengthwise forces with a resultant force P(t). The motion starts from the state of rest. The forc... more lengthwise forces with a resultant force P(t). The motion starts from the state of rest. The force P(t) increases from a quantity equal to the weight of the reservoir with liquid, smoothly approaching a constant quantity P0 at some time instant t = T. It is required that at this instant the mass center of the system be at a point specified in advance.

International Applied Mechanics, 2001

A mechanical and mathematical model of the pneumatic controller (reducer) of a spacecraft instrum... more A mechanical and mathematical model of the pneumatic controller (reducer) of a spacecraft instrumentation module is considered. This model accounts for the interaction between the gas, the moving parts of the reducer, and the environment. A method is proposed to construct stationary solutions of the relevant system of differential equations. An algorithm for realization of the method is developed. The

Journal of Spacecraft and Rockets, 2013

Journal of Guidance, Control, and Dynamics, 2008

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 1998

International Applied Mechanics, 2000

International Applied Mechanics, 1994

In programming the angular motion of a rigid body with attached elastic elements about the center... more In programming the angular motion of a rigid body with attached elastic elements about the center of mass, a key step is determination of the law governing changes over time in that part of the kinetic moment of the object which is connected with the dynamics of the elastic elements. Such a determination entails the summation of infinite series and the solution of an infinite system of differential equations. The approach traditionally employed here is to keep a finite number of terms in the series and examine a finite number of equations of motion by discarding all generalized coordinates except for a few chosen either intuitively or on the basis of certain truncation criteria. The size of the truncation error remains open to question in the latter case and is at best no smaller than the error of asymptotic methods. Below, we will assume that the character of the motions to be studied is such that, as in [3], terms higher than the first order relative to the generalized coordinates and the rates of elastic displacement can be ignored in the expression for the kinetic moment. Then the expression for the kinetic moment of the system relative to the center of mass takes the form

International Applied Mechanics, 1993

International Applied Mechanics, 2010

The paper presents an efficient method of finding the optimal program control for the reorientati... more The paper presents an efficient method of finding the optimal program control for the reorientation of a spacecraft with flexible appendages at a limited slewing rate. The appendages are incorporated into the mathematical model based on the quasistatic approximation. The problem is solved analytically by parametrizing the functional of a multipoint boundary-value problem. The optimal solution is illustrated graphically for different parts of the attainability domains

International Applied Mechanics, 1996

Soviet Applied Mechanics, 1982