Quasi-Chaplygin Systems and Nonholonimic Rigid Body Dynamics

We show that the Suslov nonholonomic rigid body problem can be regarded almost everywhere as a generalized Chaplygin system. Furthermore, this provides a new example of a multidimensional nonholonomic system which can be reduced to a Hamiltonian form by means of Chaplygin reducing multiplier. Since we deal with Chaplygin systems in the local sense, the invariant manifolds of the integrable examples are not necessary tori.Comment: minor changes, to appear in Letters in Mathematical Physic

A Generalization of Chaplygin's Reducibility Theorem

In this paper we study Chaplygin's Reducibility Theorem and extend its applicability to nonholonomic systems with symmetry described by the Hamilton-Poincare-d'Alembert equations in arbitrary degrees of freedom. As special cases we extract the extension of the Theorem to nonholonomic Chaplygin systems with nonabelian symmetry groups as well as Euler-Poincare-Suslov systems in arbitrary degrees of freedom. In the latter case, we also extend the Hamiltonization Theorem to nonholonomic systems which do not possess an invariant measure. Lastly, we extend previous work on conditionally variational systems using the results above. We illustrate the results through various examples of well-known nonholonomic systems.Comment: 27 pages, 3 figures, submitted to Reg. and Chaotic Dy

Resonant structure of space-time of early universe

A new fully quantum method describing penetration of packet from internal well outside with its tunneling through the barrier of arbitrary shape used in problems of quantum cosmology, is presented. The method allows to determine amplitudes of wave function, penetrability $T_{\rm bar}$ and reflection $R_{\rm bar}$ relatively the barrier (accuracy of the method: $|T_{\rm bar}+R_{\rm bar}-1| < 1 \cdot 10^{-15}$), coefficient of penetration (i.e. probability of the packet to penetrate from the internal well outside with its tunneling), coefficient of oscillations (describing oscillating behavior of the packet inside the internal well). Using the method, evolution of universe in the closed Friedmann--Robertson--Walker model with quantization in presence of positive cosmological constant, radiation and component of generalize Chaplygin gas is studied. It is established (for the first time): (1) oscillating dependence of the penetrability on localization of start of the packet; (2) presence of resonant values of energy of radiation $E_{\rm rad}$, at which the coefficient of penetration increases strongly. From analysis of these results it follows: (1) necessity to introduce initial condition into both non-stationary, and stationary quantum models; (2) presence of some definite values for the scale factor $a$, where start of expansion of universe is the most probable; (3) during expansion of universe in the initial stage its radius is changed not continuously, but passes consequently through definite discrete values and tends to continuous spectrum in latter time.Comment: 18 pages, 14 figures, 4 table

Integrable systems on the sphere associated with genus three algebraic curves

New variables of separation for few integrable systems on the two-dimensional sphere with higher order integrals of motion are considered in detail. We explicitly describe canonical transformations of initial physical variables to the variables of separation and vice versa, calculate the corresponding quadratures and discuss some possible integrable deformations of initial systems.Comment: 19 pages, LaTeX with AMS font

Calculation of fields and currents in the induction system with the attractive screen and the additional coil as a tool for the straightening

In the idealization of the "limiting low" frequencies of acting fields the calculated dependences for the density of the induced currents and distributed force of the attractive in the induction system with attractive screen and the external additional coil which allow to evaluate the characteristics of flowing electrodynamics processes and make recommendations for the design of the real tools for magnetic-pulse attractive of nonmagnetic thin-walled sheet metals are obtained

Diversification of lentil production

Production and processing of lentil as a valuable leguminous crop with a high content of beneficial nutrients (fiber, protein, minerals and vitamins), a low glycemic index, and a low-calorie content (295 kcal per 100 grams of raw lentils) has great potential for domestic economy. The world market of lentil is analyzed, prospects for increasing the level of its use in domestic markets are identified. An evaluation of the crop processing by an extrusion method is given. The statistical data of the Federal State Statistics Service, the Ministry of Agriculture of Russia, information materials of Russian and foreign research organizations and companies are studied. The methods of complex structural-dynamic analysis and the expert-analytical method of data processing are used. It is found that lentils contain the largest amount of protein among the rest of the plants, which is a source of essential amino acids (isoleucine and lysine), and that the use of this crop in feed production along with soya bin is promising and appropriate. Based on the analysis of gross yields of lentil in federal districts of Russia in 2010-2019 and export supplies of the crop revealed that the domestic lentil export market expanded 6.1 times, but the country’s lentil consumption decreased 1.18 times. Thus, in the current economic conditions, the issue of finding the use of lentils as a raw export product and expanding the potential for using lentils in the domestic market is relevant. It is proposed to expand the possibilities of using lentils by extruding it, which will allow to have high quality products with good biological value and consumer properties on the domestic market