Udmurt State University is a public university in the city of Izhevsk, Russia. Established in 1931, UdSU is the oldest educational institution in Udmurt Republic. In 1993, it was named among top twenty classical Russian universities, since then consistently ranks 14-16 out of 64 Russian universities.As of 2006 over 28,000 students are enrolled at the Udmurt State University, which offers 86 different majors. About 9,200 of them are full-time undergraduates. Wikipedia.
Kuznetsov S.P.,Udmurt State University
Physics-Uspekhi | Year: 2015
In connection with the problem of a convex-shaped solid body on a rough horizontal plane (the rattleback or Celtic stone), the paper discusses the validity of the nonholonomic model which postulates that the contact point has zero velocity and, hence, friction performs no mechanical work. While abstract, this model is undoubtedly constructive, similar to many idealizations commonly used in science. Despite its energy-conserving nature, the model does not obey Liouville's theorem on phase volume conservation, thus allowing the occurrence in the phase space of objects characteristic of dissipative dynamics (attractors) and thereby leading to phenomena like the spontaneous reversal of rotations. Nonholonomic models, intermediate between conservative and dissipative systems, should take their deserved place in the general picture of the modern theory of dynamical systems. © 2015 Uspekhi Fizicheskikh Nauk, Russian Academy of Sciences.
Zaitsev V.A.,Udmurt State University
Systems and Control Letters | Year: 2016
We consider a nonlinear control system with periodic coefficients. We study the problem of asymptotic stabilization of the equilibrium x=0 of the closed-loop system by state feedback. We assume that the free dynamic system possesses a periodic Lyapunov function ensuring Lyapunov stability of the equilibrium x=0. We have developed a method for constructing a damping control for affine systems with periodic coefficients based on a generalization of weak Jurdjevic-Quinn conditions, using an extension of the notion of the commutator to non-stationary vector fields. Using this approach, we obtain sufficient conditions for uniform local and global asymptotic stabilization of general nonlinear systems, in particular, affine control systems, with periodic coefficients. Stabilization results generalize known results for time-invariant systems to time-varying periodic systems. © 2016 Elsevier B.V. All rights reserved.
Kondratyev B.P.,Udmurt State University
Solar System Research | Year: 2011
A flexible and informative vector approach to the problem of physical libration of the rigid Moon has been developed in which three Euler differential equations are supplemented by 12 kinematic ones. A linearized system of equations can be split into an even and odd systems with respect to the reflection in the plane of the lunar equator, and rotational oscillations of the Moon are presented by superposition of librations in longitude and latitude. The former is described by three equations and consists of unrestricted oscillations with a period of T1 = 2.878 Julian years (amplitude of 1.855″) and forced oscillations with periods of T2 = 27.201 days (15.304″), one stellar year (0.008″), half a year (0.115″), and the third of a year (0.0003″) (five harmonics altogether). A zero frequency solution has also been obtained. The effect of the Sun on these oscillations is two orders of magnitude less than that of the Earth. The libration in latitude is presented by five equations and, at pertrubations from the Earth, is described by two harmonics of unrestricted oscillations (T5 ≈ 74.180 Julian years, T6 ≈ 27.347 days) and one harmonic of forced oscillations (T3 = 27.212 days). The motion of the true pole is presented by the same harmonics, with the maximum deviation from the Cassini pole being 45.3″. The fifth (zero) frequency yields a stationary solution with a conic precession of the rotation axis (previously unknown). The third Cassini law has been proved. The amplitudes of unrestricted oscillations have been determined from comparison with observations. For the ratio sinI/sin(I+i) ≈ 0.2311 the theory gives 0.2319, which confirms the adequacy of the approach. Some statements of the previous theory are revised. Poinsot's method is shown to be irrelevant in describing librations of the Moon. The Moon does not have free (Euler) oscillations; it has oscillations with a period of T5 ≈ 74.180 Julian years rather than T ≈ 148.167 Julian years. © 2011 Pleiades Publishing, Ltd.
Petrov N.N.,Udmurt State University
Automation and Remote Control | Year: 2014
We consider two linear nonstationary pursuit-evasion problems with one evader and a group of pursuers under the conditions that the players have equal dynamic abilities and that the evader cannot leave a certain set. We prove that if the number of pursuers is less than the space dimension, then the evader can avoid capture in the interval [t 0,∞). © 2014 Pleiades Publishing, Ltd.
Chausov F.F.,Udmurt State University
Bulletin of the Russian Academy of Sciences: Physics | Year: 2013
A method for protecting steel against oxygen corrosion in water solutions using an inhibitor that selectively reacts with a metal surface in corrosion centers is proposed. 1-hydroxyethylidenediphosphonatozincate, which contains a localized π bond between its phosphorus and oxygen atoms, is used as the inhibitor in combination with magnesium ions at an oxygen concentration of 0.1 to 6.0 mg dm-3 and pH in a water solution of 5.8 to 11.1. A 91-93% degree of protection is achieved at an inhibitor concentration of 6 mg dm -3. © 2013 Allerton Press, Inc.