Conditions of the Maximum Principle in the Problem of Optimal Control over an Aggregate of Dynamic Systems and Their Application to Solution of the Problems of Optimal Control of Spacecraft Motion

The necessary first-order conditions of strong local optimality (conditions of maximum principle) are considered for the problems of optimal control over a set of dynamic systems. To derive them a method is suggested based on the Lagrange principle of removing constraints in the problems on a conditional extremum in a functional space. An algorithm of conversion from the problem of optimal control of an aggregate of dynamic systems to a multipoint boundary value problem is suggested for a set of systems of ordinary differential equations with the complete set of conditions necessary for its solution. An example of application of the methods and algorithm proposed is considered: the solution of the problem of constructing the trajectories of a spacecraft flight at a constant altitude above a preset area (or above a preset point) of a planet's surface in a vacuum (for a planet with atmosphere beyond the atmosphere). The spacecraft is launched from a certain circular orbit of a planet's satellite. This orbit is to be determined (optimized). Then the satellite is injected to the desired trajectory segment (or desired point) of a flyby above the planet's surface at a specified altitude. After the flyby the satellite is returned to the initial circular orbit. A method is proposed of correct accounting for constraints imposed on overload (mixed restrictions of inequality type) and on the distance from the planet center: extended (nonpointlike) intermediate (phase) restrictions of the equality type.     

A Series of Proton Flares in July 1985 from Observations by the Prognoz-10 Satellite and Vega-1, 2 Spacecraft

The enhancements of solar protons with an energy of more than 30 MeV, originating from flares in one active region and observed simultaneously aboard three spacecraft Vega-1, 2 and Prognoz-10 in July 1985, are analyzed and approximated in this work by using the reflection model [2]. The numerical values of several physical parameters (the parameters of distribution of solar cosmic ray (SCR) particles inside heliosphere traps, the coefficients of trap transparency) that are not observed by direct measurements are estimated.     

Energy Spectrum of Galactic 10–100 MeV Protons in Quiet Sun Periods

The dynamics of the proton energy spectrum during the solar cycle is studied. The spectra were determined by 1–100 MeV particle fluxes measured by different instruments mounted aboard the Earth's IMP-8 satellite for more than one hundred quiet-time intervals in the period between 1974 and 1991. The galactic branch of the spectra (E _p > 10 MeV) constructed for every quiet interval was fitted by a power law function, J =CE . The theory predicts that in the 1–100 MeV energy range, where the adiabatic cooling of particles is dominant, = 1, while we have derived a double-peak distribution. The main maximum has the mean value = 1.35. The mean value of the second, much weaker maximum, is = 0.95. Within the main maximum, values are distributed in accordance with the Gaussian law with a standard deviation D/ = 0.12. The substantial difference of from unity requires the elaboration of a new model of modulation processes in the inner heliosphere. The values corresponding to the second maximum show that modulation processes correspond sometimes to theoretical conceptions. It is shown that correlates weakly with parameters A and describing the solar branch of the spectrum (J(E) = AE ^–). At the same time, a more significant correlation is observed between and the solar activity index, R _z, the counting rate of the Deep River neutron monitor, and the energy value in the minimum of the energy spectrum flux, E _min.     

Single-Axis Solar Orientation of a Satellite of the Earth

The possibility of using the mode of single-axis solar orientation is considered for a satellite placed into a nearly circular orbit with an altitude of 900 km and bearing a solar sail. The satellite (together with the sail) has an axisymmetric structure, its symmetry axis being the principal central axis of the maximum moment of inertia. The center of the sail pressure lies on this axis and is displaced with respect to the satellite's center of mass. The symmetry axis of the satellite is set to the Sun so that its center of mass would be located between the Sun and the pressure center and would rotate around this axis with an angular velocity of a few degrees per second. The satellite's axis of symmetry makes a slow precession under the action of the gravitational moment and the moment of light pressure forces. Though the maximum magnitudes of these moments are comparable, the moment of the light pressure forces dominates and controls the precession in such a way that the symmetry axis orientation to the Sun remains unchanged.     

Synthesis of biomass and utilization of plants wastes in a physical model of biological life-support system

The paper considers problems of biosynthesis of higher plants' biomass and "biological incineration" of plant wastes in a working physical model of biological LSS. The plant wastes are "biologically incinerated" in a special heterotrophic block involving Californian worms, mushrooms and straw. The block processes plant wastes (straw, haulms) to produce soil-like substrate (SLS) on which plants (wheat, radish) are grown. Gas exchange in such a system consists of respiratory gas exchange of SLS and photosynthesis and respiration of plants. Specifics of gas exchange dynamics of high plants--SLS complex has been considered. Relationship between such a gas exchange and PAR irradiance and age of plants has been established. Nitrogen and iron were found to the first to limit plants' growth on SLS when process conditions are deranged. The SLS microflora has been found to have different kinds of ammonifying and denitrifying bacteria which is indicative of intensive transformation of nitrogen-containing compounds. The number of physiological groups of microorganisms in SLS was, on the whole, steady. As a result, organic substances--products of exchange of plants and microorganisms were not accumulated in the medium, but mineralized and assimilated by the biocenosis. Experiments showed that the developed model of a man-made ecosystem realized complete utilization of plant wastes and involved them into the intrasystem turnover.     

An Analysis of the Low-Frequency Component in Measurements of Angular Velocity and Microacceleration onboard the Foton-12 Satellite

We compare the results of two methods used to determine the angular velocity of the Foton-12 satellite and the low-frequency component of microaccelerations onboard it. The first method is based on reconstruction of the satellite's rotational motion using the data of onboard measurements of the strength of the Earth's magnetic field. The motion (time dependence of the orientation parameters and angular velocity) was found from the condition of best approximation of the measurement data by the functions calculated along the solutions to equations of attitude motion of the satellite. The solutions found were used to calculate the quasistatic component of microaccelerations at certain points of the satellite, in particular, at the point of location of an accelerometer of the QSAM system. Filtration of the low-frequency component of the angular velocity and microacceleration from the data of measurements by a sensor of angular velocity and by the accelerometer of this system served as a second method. The filtration was made using the discrete Fourier series. A spectral analysis of the functions representing the results of determining the angular velocity and microacceleration by both methods is performed. Comparing the frequencies and amplitudes of the harmonic component of these functions allowed us to estimate the accuracy of measurements made by the QSAM system in the low-frequency range.     

Effect of variable thermal properties of the solid phase on composite solid propellant combustion

Effects of variable thermal properties (specific heat and thermal conductivity) of the solid phase on the combustion of composite solid propellants are studied analytically. Both steady and unsteady burning are considered. It is shown that the effects of variable thermal properties are small and can be accounted for by choosing proper average values of specific heat and thermal conductivity.     

Plasma irregularities in unstable outer ionosphere according to the Intercosmos-Bulgaria-1300 satellite data

The results of the satellite low-latitude and mid-latitude measurements of the disturbed plasma concentration, electron temperature, and quasi-stable electric field at heights of ～900 km after sunset are discussed. It is shown that the sharp fronts of changes in the electron temperature and plasma density observed in the experiment onboard the Intercosmos-Bulgaria-1300 satellite in the low-latitude (and equatorial) outer ionosphere can be related to damping of the oscillations of plasma electrons at local decreases of the plasma density (plasma “pits”) and formation of the vortex plasma structures at density and temperature gradients, which promotes conservation of ionosphere irregularities and makes the fronts of concentration variations steeper. Nonmonotonic variations in the plasma conductivity for the ionosphere currents in unstable plasma can be a cause of observed nonmonotonic disturbances of the vertical component of the “constant” electric field.     

Venus Express: Scientific goals, instrumentation, and scenario of the mission

The first European mission to Venus (Venus Express) is described. It is based on a repeated use of the Mars Express design with minor modifications dictated in the main by more severe thermal environment at Venus. The main scientific task of the mission is global exploration of the Venusian atmosphere, circumplanetary plasma, and the planet surface from an orbiting spacecraft. The Venus Express payload includes seven instruments, five of which are inherited from the missions Mars Express and Rosetta. Two instruments were specially designed for Venus Express. The advantages of Venus Express in comparison with previous missions are in using advanced instrumentation and methods of remote sounding, as well as a spacecraft with a broad spectrum of capabilities of orbital observations.     

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.