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## Optimization of interorbital three-dimensional transfer trajectories for stage spacecraft

### Automation and Remote Control (2007-08-01) 68: 1372-1390 , August 01, 2007

Problems of three-dimensional trajectory optimization of transfers for stage spacecraft and spacecraft with auxiliary fuel tank (AFT) from the low circuit orbit of the Earth’s artificial satellite (EAS) into the geostationary orbit and optimization problems of fuel distribution in stages or tanks are solved. Control of spacecraft motion is conducted by jet engines of bounded thrust; stage engines can have different characteristics, i.e., thrust-to-weight ratio and specific thrust. The used stage or auxiliary fuel tank is detached on the passive segment. Detachment is considered to be instantaneous, if the spacecraft position and velocity do not change at the detachment instant and the mass decreases in jumping mode. The mass of detached tanks is considered proportionate to the mass of consumed fuel; the mass of engine and auxiliary constructions, to thrust-to-weight ratio. The useful mass of the spacecraft with the limited time of transfer is maximized. The considered problems are intricate nonlinear optimal control problems with discontinuous phase variables. They are formalized as optimal control problems by a union of dynamic systems and are solved on the basis of the corresponding principle of the maximum. In this paper, boundary-value problems of the principle of the maximum are numerically solved by the shooting method. The choice of computing schemes of the shooting method and solution to systems of nonlinear equations is conducted by using a series of auxiliary problems.

## A method for solving the problem of isometric realization of developments

### Journal of Mathematical Sciences (2008-02-01) 149: 971-995 , February 01, 2008

We suggest a new algorithmic solution for the problem of isometric realization of developments. For any development, a system of polynomial equations is composed such that its solutions are, in some sense, in bijective correspondence with all possible isometric realizations of the development. An important advantage of this method is the fact that it can be used in practical computations.

## Strong closure operators on the set of partial Boolean functions

### Doklady Mathematics (2008-04-01) 77: 288-289 , April 01, 2008

## Mathematical Analysis of Problems in the Natural Sciences

### Mathematical Analysis of Problems in the Natural Sciences (2011-01-01) , January 01, 2011

## Kronecker indices of Lie algebras and invariants degrees estimate

### Moscow University Mathematics Bulletin (2011-03-23) 66: 25-29 , March 23, 2011

The concept of Kronecker indices of a Lie algebra as integer characteristics naturally connected to its structure tensor is introduced. A lower bound for the degrees of polynomial invariants of the co-adjoint action in terms of Kronecker indices is proved.

## Constructing Pontryagin extremals for the optimal control problem of asteroid fly-by

### Automation and Remote Control (2009-09-01) 70: 1499-1513 , September 01, 2009

We consider the problem of constructing Pontryagin extremals for the optimal control task of asteroid fly-by. This problem is a part of a large optimization problem posed on the Third Global Trajectory Optimization Competition. Information about the competition and problem details can be found at http://www2.polito.it/eventi/gtoc3 .

## On oscillations of a semi-infinite rotating liquid with its free surface excited by moving sources

### Computational Mathematics and Mathematical Physics (2006-05-01) 46: 891-906 , May 01, 2006

Propagation of small perturbations in a homogeneous inviscid liquid rotating with a constant angular velocity in the lower half-space is considered. The source of excitation is a plane wave traveling on the free surface of the liquid. The explicit analytical solution to the problem is constructed. Uniqueness and existence theorems are proved. The wave pattern in the liquid at large times is examined.

## Homogenizaton of a Nonhomogeneous Signorini Problem for the Poisson Equation in a Periodically Perforated Domain

### Differential Equations (2003-03-01) 39: 387-396 , March 01, 2003

## Instability of Multidimensional Contrast Structures

### Differential Equations (2002-02-01) 38: 235-248 , February 01, 2002

## Optimum throughput of a system of product logistics between two markets

### Moscow University Computational Mathematics and Cybernetics (2014-07-01) 38: 128-133 , July 01, 2014

A model of a network market with two nodes and perfect competition is analyzed. The equilibrium depending on the throughput capacity of a system of product logistics is determined, and properties of the total welfare function are examined. A method is proposed for finding the optimum throughput capacity of a system of product logistics between two markets from the point of view of the total welfare.