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.     

Application of a magnetohydrodynamic element in the control loop of a rotating spacecraft with cavities partially filled with liquid

This paper is a continuation of [1–3] and a generalization of the results for a rotating spacecraft with cavities partially filled with liquid and equipped with an operational magnetohydrodynamic (MHD) element in the loop of its attitude control. This element makes possible the creation of hingeless systems of stabilization and orientation that do not require rocket propellant consumption. The application of an MHD element is considered for stabilization in the mode of spin-up of a spacecraft not having gyroscopic stability.     

Multi-structural estimation of an integrated navigation system of a reusable spacecraft

An approach to the synthesis of an integrated navigation system is considered for a reusable space-craft that performs an arbitrary spatial maneuver under the conditions of internal and external disturbances. The offered approach provides for a noise-suppressing solution of the navigation problem, both in a regular mode of spacecraft motion, and during its descent along the unplanned trajectory.     

The use of solutions to problems of spacecraft trajectory optimization in impulse formulation when solving the problems of optimal control of trajectories of a spacecraft with limited thrust engine: I

In this first part of our paper, it is suggested to use solutions to boundary value problems in the optimization problems (in impulse formulation) for spacecraft trajectories in order to obtain the initial approximation, when boundary value problems of the maximum principle are solved numerically by the shooting method. The technique suggested is applied to the problems of optimal control over motion of the center of mass of a spacecraft controlled by the thrust vector of jet engine with limited thrust in an arbitrary gravitational field in a vacuum. The method is based on a modified (in comparison to the classic scheme) shooting method computation together with the method of continuation along a parameter (maximum reactive acceleration, initial thrust-to-weight ratio, or any other parameter equivalent to them). This technique allows one to obtain the initial approximation with a high precision, and it is applicable to a wide range of optimal control problems solved using the maximum principle, if the impulse formulation makes sense for these problems.     

An alternative algorithm for the spacecraft information system with magnetometer and solar sensor

The possibility of identification of motion parameters of a low-orbit spacecraft using readings of a three-axis magnetometer and solar position sensor, without integration of the Euler’s dynamic equations or direct measurement of the object’s angular velocity, is considered.     

Optimization of interplanetary trajectories for spacecraft with ideally regulated engines using the continuation method

The problem of optimization of interplanetary trajectories is considered for spacecraft with a small-thrust ideally regulated engine. When the maximum principle is used, determination of the optimal trajectory is reduced to solution of a two-point boundary value problem for a system of ordinary differential equations. In order to solve this boundary value problem, the method of continuation in parameter is used, and with the help of it the formal reduction of the boundary value problem to a Cauchy problem is performed. Different variants of the continuation method are considered, including the method of continuation in the gravitational parameter which allows one to find extreme trajectories with a preset angular distance. The issues of numerical realization of the continuation method are discussed, and numerical examples of its use for solving the problems of optimization of interplanetary trajectories are presented.     

Application of information criteria to control the structurally uncertain navigation system of a reusable spacecraft

The problem of attitude control of a gyro-stabilized platform with the structurally uncertain drift model is solved. The solution is realized in two stages. At the first stage, on the basis of the obtained stochastic model of the reusable spacecraft navigation system, the drift model of gyro-stabilized platform is identified. At the second stage, the control of its spatial orientation is synthesized with regard to the found drift model. The results of numerical simulation are presented in conclusion.     

Ballistics, navigation, and motion control for a spacecraft during its landing on the surface of Phobos

Basic concepts and algorithms laid as foundations of the scheme of landing on the Martian moon Phobos (developed for the Phobos-Grunt project) are presented. The conditions ensuring the landing are discussed. Algorithms of onboard navigation and control are described. The equations of spacecraft motion with respect to Phobos are considered, as well as their use for correction of the spacecraft motion. The algorithm of estimation of the spacecraft’s state vector using measurements with a laser altimeter and Doppler meter of velocity and distance is presented. A system for modeling the landing with a firmware complex including a prototype of the onboard computer is described.     

Calculation of quasisynchronous orbits of a spacecraft around Phobos for solving the problem of landing on its surface

The problem of selecting quasi-synchronous orbits of a spacecraft around Phobos is considered. These quasi-synchronous orbits are far (with respect to the Hill’s sphere) quasi-satellite orbits with retrograde rotation in the restricted three body problem. The orbit should pass through a given point at a specified time instant. It should also possess a property of minimum distance from the Phobos surface at every passage above the region of planned landing. The equations of dynamics are represented in the form describing the orbit as a combination of motions in two drifting ellipses, inner and outer ellipses. The center of the outer ellipse is located on the inner ellipse. A formula is derived that relates averaged values of half-axes of the inner and outer ellipses. It is used for construction of the first approximation of numerically designed orbit, which makes it possible to simplify and speed up the computing process. The tables of initial conditions obtained as a result of calculations are presented.     

Semianalytic estimations of boundaries of a corridor of spacecraft entry into the planetary atmosphere at considerable values of permissible maximum overload

Trajectories of spacecraft entry into the planetary atmosphere with a velocity essentially exceeding the first cosmic velocity are considered. An estimation of the minimum permissible value of the altitude of conditional pericenter (perigee in the case of the Earth), at which extreme permissible value of maximum overload is reached, is of the main interest. Semianalytic formulas including the cases of considerable values of the maximum overload are suggested.     

Trajectories for missions of low-thrust spacecraft aimed at delivery of soil samples from main belt asteroids and Phobos

Trajectories of spacecraft with electro-jet low-thrust engines are studied for missions planning to deliver samples of matter from small bodies of the Solar System: asteroids Vesta and Fortuna, and Martian moon Phobos. Flight trajectories are analyzed for the mission to Phobos, the limits of optimization of payload spacecraft mass delivered to it are determined, and an estimate is given to losses in the payload mass when a low-thrust engine with constant outflow velocity is used. The model of an engine with ideally regulated low thrust is demonstrated to be convenient for calculations and analysis of flight trajectories of a low-thrust spacecraft.     

Vertical distribution of the power of short- and long-period oscillations in a sunspot and in surrounding magnetic elements

We present the results of processing three 256-min series of observations of quasi-periodic oscillations of the field of line-of-sight velocities in three sunspots. The Doppler shifts were determined simultaneously for six spectral lines formed at different heights in the solar atmosphere. In addition to the well-known high-frequency (periods of 3–5 min) oscillations, a band of low-frequency oscillations with periods of 60–80 min is revealed in the spectra of the sunspot umbra and magnetic elements located in immediate proximity of the sunspot. Unlike the short-period modes, the power of the long-period mode of line-of-sight velocity oscillations in the sunspot decreases sharply with height: these oscillations are distinctly seen in the line formed at a height of 200 km and almost are not seen in the line with the formation height of 500 km. This is indicative of different physical nature of the short-period and long-period oscillations of a sunspot. If the former are caused by slow magnetosonic waves within the field tube of the spot, the latter are representative of global vertical-radial oscillations of a magnetic element (spot, pore) as a whole near the position of a stable equilibrium.     

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.     

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.     

Multiple continuous coverage of the earth based on multi-satellite systems with linear structure

A new and wider definition is given to multi-satellite systems with linear structure (SLS), and efficiency of their application to multiple continuous coverage of the Earth is substantiated. Owing to this widening, SLS have incorporated already well-recognized “polar systems” by L. Rider and W.S. Adams, “kinematically regular systems” by G.V. Mozhaev, and “delta-systems” by J.G. Walker, as well as “near-polar systems” by Yu.P. Ulybyshev, and some other satellite constellations unknown before. A universal method of SLS optimization is presented, valid for any values of coverage multiplicity and the number of satellites in a system. The method uses the criterion of minimum radius of a circle seen from a satellite on the surface of the globe. Among the best SLS found in this way there are both systems representing the well-known classes mentioned above and new orbit constellations of satellites.