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181. http://ics.org.ru/upload/iblock/336/170-statistical-irreversibility-of-the-kac-reversible-circular-model_en.pdf
... Statistical Irreversibility of the Kac Reversible Circular Mo del Valery V. Kozlov* V.A. Steklov Mathematical Institute Russian Academy of Sciences ul. Gubkina 8, Moscow, 119991 Russia Received Octob er 29, 2010; accepted Decemb er 4, 2010 Abstract--The Kac circular model is a discrete dynamical system which has the property of recurrence and reversibility. ... However, this p oint of view contradicts the initial prop erty of reversibility of the equations of motion for mechanical systems. ...
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Ссылки http://ics.org.ru/upload/iblock/336/170-statistical-irreversibility-of-the-kac-reversible-circular-model_en.pdf -- 203.6 Кб -- 28.10.2015
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182. http://ics.org.ru/upload/iblock/b4d/168-on-the-model-of-non-holonomic-billiard_ru.pdf
ISSN 1560-3547, Regular and Chaotic Dynamics, 2011, Vol. ... MSC2010 numbers: 34D20, 70E40, 37J35 DOI: 10.1134/S1560354711060062 Keywords: billiard, impact, point map, nonintegrability, periodic solution, nonholonomic constraint, integral of motion 1. ... 2 Vol. ... Then if one of the semi-axes of the cylinder's base tends to zero (b2 0) we get the problem on nonholonomic bil liard inside a flat strip with the fol lowing law of reflection 0 0 -1 = 0 cos - sin 0 - sin - cos V where V = (vn , v , ua ). ...
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Ссылки http://ics.org.ru/upload/iblock/b4d/168-on-the-model-of-non-holonomic-billiard_ru.pdf -- 200.9 Кб -- 28.10.2015
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183. http://ics.org.ru/upload/iblock/c96/169-the-vlasov-kinetic-equation-dynamics-of-continuum-and-turbulence_ru.pdf
... The Vlasov Kinetic Equation, Dynamics of Continuum and Turbulence Valery V. Kozlov * V.A. Steklov Mathematical Institute Russian Academy of Sciences ul. Gubkina 8, Moscow, 119991 Russia Received January 6, 2011; accepted March 3, 2011 Abstract--We consider a continuum of interacting particles whose evolution is governed by the Vlasov kinetic equation. ... The density of the medium is the function of x, u and t. It is non-negative, and (x, u, t) dx du = m is the mass of matter. ... Vol. ...
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Ссылки http://ics.org.ru/upload/iblock/c96/169-the-vlasov-kinetic-equation-dynamics-of-continuum-and-turbulence_ru.pdf -- 325.0 Кб -- 28.10.2015
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184. http://ics.org.ru/upload/iblock/c61/166-on-invariant-manifolds-of-nonholonomic-systems_en.pdf
... On Invariant Manifolds of Nonholonomic Systems Valery V. Kozlov * V.A. Steklov Mathematical Institute Russian Academy of Sciences ul. Gubkina 8, Moscow, 119991 Russia Received December 27, 2011; accepted January 23, 2012 Abstract--Invariant manifolds of equations governing the dynamics of conservative nonholonomic systems are investigated. ... 2 2012 ON INVARIANT MANIFOLDS OF NONHOLONOMIC SYSTEMS 135 We emphasize that the system of differential equations (2.3) is closed and has the form (1.6). ...
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Ссылки http://ics.org.ru/upload/iblock/c61/166-on-invariant-manifolds-of-nonholonomic-systems_en.pdf -- 240.1 Кб -- 28.10.2015
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185. http://ics.org.ru/upload/iblock/ad1/165-two-non-holonomic-integrable-problems-tracing-back-to-chaplygin_ru.pdf
... The systems consist of a spherical shell that rolls on a plane; within the shell there is a ball or Lagrange's gyroscope. ... For this problem the equations of motion were integrated by Chaplygin. ... Equations of Motion Consider a system that consists of two bodies: 1) a spherical shell rolling on a horizontal plane inside which there is a spherical cavity such that its center coincides with the shell's center and 2) a ball placed into the spherical cavity of the shell (Fig. ... 2 2012 Vol. ...
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Ссылки http://ics.org.ru/upload/iblock/ad1/165-two-non-holonomic-integrable-problems-tracing-back-to-chaplygin_ru.pdf -- 151.3 Кб -- 28.10.2015
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186. http://ics.org.ru/upload/iblock/a47/164-generalized-chaplygin-s-transformation-and-explicit-integration-of-a-system-with-a-spherical-support_ru.pdf
ISSN 1560-3547, Regular and Chaotic Dynamics, 2012, Vol. ... 37J60, 37J35, 70E18, 70F25, 70H45 DOI: 10.1134/S1560354712020062 Keywords: nonholonomic mechanics, spherical support, Chaplygin ball , explicit integration, isomorphism, bifurcation analysis Contents INTRODUCTION 1 CHAPLYGIN'S TRANSFORMATION IN THE PROBLEM OF A BALL 'S ROLLING MOTION ON A PLANE 1.1 1.2 1.3 1.4 1.5 * ** *** 171 172 172 173 174 175 176 Equations of ... Ballbots use a large ball as core of its propulsion system. ...
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Ссылки http://ics.org.ru/upload/iblock/a47/164-generalized-chaplygin-s-transformation-and-explicit-integration-of-a-system-with-a-spherical-support_ru.pdf -- 485.8 Кб -- 28.10.2015
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187. http://ics.org.ru/upload/iblock/331/161-chaplygin-ball-over-a-fixed-sphere-an-explicit-integration_ru.pdf
... JURGEN MOSER ґ 80 Chaplygin Ball over a Fixed Sphere: an Explicit Integration A. Borisov1 * , Yu. ... The system generalizes the classical nonholonomic Chaplygin sphere problem and it is shown to be integrable for one special ratio of radii of the spheres. ... In [4] S.A. Chaplygin obtained the equations of motion, proved their integrability and p erformed their reduction to quadratures by using spheroconic coordinates on the Poisson sphere as separating variables. ... 2.6) Second integrable case. ...
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Ссылки http://ics.org.ru/upload/iblock/331/161-chaplygin-ball-over-a-fixed-sphere-an-explicit-integration_ru.pdf -- 284.0 Кб -- 28.10.2015
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188. http://ics.org.ru/upload/iblock/c6e/162-coupled-motion-of-a-rigid-body-and-point-vortices-on-a-two-dimensional-spherical-surface_ru.pdf
ISSN 1560-3547, Regular and Chaotic Dynamics, 2010, Vol. ... MSC2000 numbers: 76B47, 70Exx, 70Hxx DOI: 10.1134/S1560354710040040 Key words: hydro dynamics on a sphere, coupled bo dy-vortex system, mass vortex, equations of motion, integrability Contents INTRODUCTION 1 442 FLUID DYNAMICS ON TWO-DIMENSIONAL SURFACES 443 1.1 The Dynamics of Ideal Fluid on Two-Dimensional Surfaces . ... Equation of motion. ... Studying various cases of the motion of a rigid b ody and p oint vortices on the sphere. ...
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Ссылки http://ics.org.ru/upload/iblock/c6e/162-coupled-motion-of-a-rigid-body-and-point-vortices-on-a-two-dimensional-spherical-surface_ru.pdf -- 299.7 Кб -- 28.10.2015
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189. http://ics.org.ru/upload/iblock/365/160-multiparticle-systems-the-algebra-of-integrals-and-integrable-cases_en.pdf
... The most general form of the additional integral of motion, which we term the Jacobi integral, is presented for such systems. ... MSC2000 numbers: 70Hxx, 70G65 DOI: 10.1134/S1560354709010043 Key words: multiparticle systems, Jacobi integral Contents INTRODUCTION 19 1 N -BODY PROBLEM 19 1.1 Integrals of Motion, Reduction, and the Algebra of Integrals . ... 2.3 The Rosochatius System . ... i - j )2 (4.18) System (4.18) has three Casimir functions 2 , (M, ), ?2 and at least one integral of motion (4.7)...
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Ссылки http://ics.org.ru/upload/iblock/365/160-multiparticle-systems-the-algebra-of-integrals-and-integrable-cases_en.pdf -- 473.5 Кб -- 28.10.2015
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190. http://ics.org.ru/upload/iblock/580/159-the-hamiltonian-dynamics-of-self-gravitating-liquid-and-gas-ellipsoids_ru.pdf
ISSN 1560-3547, Regular and Chaotic Dynamics, 2009, Vol. 14, No. 2, pp. 179-217. c Pleiades Publishing, Ltd., 2009. The Hamiltonian Dynamics of Self-gravitating Liquid and Gas Ellipsoids A. V. Borisov* , A. A. Kilin** , and I. S. Mamaev* Institute of Computer Science, Udmurt State University, ul. Universitetskaya 1, Izhevsk, 426034 Russia Received August 3, 2008; accepted Decemb er 1, 2008 ** Abstract--The dynamics of self-gravitating liquid and gas ellipsoids is considered. A literary survey and authors'
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Ссылки http://ics.org.ru/upload/iblock/580/159-the-hamiltonian-dynamics-of-self-gravitating-liquid-and-gas-ellipsoids_ru.pdf -- 886.6 Кб -- 28.10.2015
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191. http://ics.org.ru/upload/iblock/d07/157-isomorphisms-of-geodesic-flows-on-quadrics_en.pdf
ISSN 1560-3547, Regular and Chaotic Dynamics, 2009, Vol. ... On a fixed energy level E = h for = 1 the flow of the Jacobi problem is trajectory equivalent to the flow of the Brun system (2.5) with the Hamiltonian 1 h (M , I-1 M ) - ( , I ) 2 det I on the zero level of the Hamiltonian HB = 0 and K1 = 1, K2 = 0. ... 4-5 2009 (3.13) Vol. ... Consider the Brun system with the Hamiltonian and the additional integral of the form H= Let H = 0, I-1/2 , ( , I-1 ) F = f, 2 = 1, det I3/2 I ( , I ) (M , ) = 0. ...
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Ссылки http://ics.org.ru/upload/iblock/d07/157-isomorphisms-of-geodesic-flows-on-quadrics_en.pdf -- 377.6 Кб -- 28.10.2015
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192. http://ics.org.ru/upload/iblock/a44/155-superintegrable-system-on-a-sphere-with-the-integral-of-higher-degree_ru.pdf
... RESEARCH ARTICLES Sup erintegrable System on a Sphere with the Integral of Higher Degree A. V. Borisov* , A. A. Kilin** , and I. S. Mamaev*** Institute of Computer Science, Udmurt State University, ul. ... Al l trajectories of the system (2.3) are closed. ... The integral J is the Jacobi integral existing for any natural systems with a homogeneous p otential of degree = -2, and the integrals G and J2 are generalizations of the corresp onding integrals for the problem of N Hooke centers on a sphere. ...
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Ссылки http://ics.org.ru/upload/iblock/a44/155-superintegrable-system-on-a-sphere-with-the-integral-of-higher-degree_ru.pdf -- 126.3 Кб -- 28.10.2015
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193. http://ics.org.ru/upload/iblock/7d3/154-lagrange-s-identity-and-its-generalizations_en.pdf
ISSN 1560-3547, Regular and Chaotic Dynamics, 2008, Vol. ... Gubkina 8, Moscow, 119991 Russia Received January 14, 2008; accepted February 7, 2008 Abstract--The famous Lagrange identity expresses the second derivative of the moment of inertia of a system of material points through the kinetic energy and homogeneous potential energy. ... MSC2000 numbers: 37A60, 82B30, 82CXX DOI: 10.1134/S1560354708020019 Key words: Lagrange's identity, quasi-homogeneous function, dilations, Vlasov's equation 1. ...
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Ссылки http://ics.org.ru/upload/iblock/7d3/154-lagrange-s-identity-and-its-generalizations_en.pdf -- 145.8 Кб -- 28.10.2015
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194. http://ics.org.ru/upload/iblock/e41/152-absolute-and-relative-choreographies-in-rigid-body-dynamics_ru.pdf
ISSN 1560-3547, Regular and Chaotic Dynamics, 2008, Vol. ... Universitetskaya 1, Izhevsk, 426034 Russia Received March 14, 2007; accepted Novemb er 28, 2007 Abstract--For the classical problem of motion of a rigid bo dy about a fixed point with zero area integral, we present a family of solutions that are perio dic in the absolute space. ... INTRODUCTION This pap er is devoted to the search and study of p eriodic solutions in the problem on the motion of a heavy rigid b ody with a fixed p oint. ...
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Ссылки http://ics.org.ru/upload/iblock/e41/152-absolute-and-relative-choreographies-in-rigid-body-dynamics_ru.pdf -- 448.2 Кб -- 28.10.2015
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195. http://ics.org.ru/upload/iblock/025/150-stability-of-steady-rotations-in-the-nonholonomic-routh-problem_ru.pdf
... NONHOLONOMIC MECHANICS Stability of Steady Rotations in the Nonholonomic Routh Problem A. V. Borisov* , A. A. Kilin** , and I. S. Mamaev* Institute of Computer Science, Udmurt State University, ul. Universitetskaya 1, Izhevsk, 426034 Russia Received Octob er 4, 2007; accepted January 16, 2008 ** Abstract--We have discovered a new first integral in the problem of motion of a dynamically symmetric ball, sub ject to gravity, on the surface of a paraboloid. ... Phase p ortrait of the system (18). ...
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Ссылки http://ics.org.ru/upload/iblock/025/150-stability-of-steady-rotations-in-the-nonholonomic-routh-problem_ru.pdf -- 393.4 Кб -- 28.10.2015
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196. http://ics.org.ru/upload/iblock/283/149-gauss-principle-and-realization-of-constraints_en.pdf
... 2008. NONHOLONOMIC MECHANICS Gauss Principle and Realization of Constraints V. V. Kozlov* V.A. Steklov Institute of Mathematics, Russian Academy of Sciences, ul. ... From (3) it immediately follows that an actual motion is a virtual one. ... x (10) If one considers this relation as a definition of virtual motions, then the generalized Gauss principle leads to the equation x=- Е ,x x, (x, x) V x which also has the integral of energy, but differs from the initial equation (9). ...
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Ссылки http://ics.org.ru/upload/iblock/283/149-gauss-principle-and-realization-of-constraints_en.pdf -- 145.2 Кб -- 28.10.2015
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197. http://ics.org.ru/upload/iblock/099/147-interaction-between-kirchhoff-vortices-and-point-vortices-in-an-ideal-fluid_ru.pdf
ISSN 1560-3547, Regular and Chaotic Dynamics, 2007, Vol. ... RESEARCH ARTICLES Interaction between Kirchhoff Vortices and Point Vortices in an Ideal Fluid A. V. Borisov* and I. S. Mamaev ** Institute of Computer Science, Udmurt State University, Universitetskaya ul. 1, 426034 Izhevsk, Russia Received March 1, 2005; accepted January 14, 2006 Abstract--We consider the interaction of two vortex patches (elliptic Kirchhoff vortices) which move in an unbounded volume of an ideal incompressible fluid. ...
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Ссылки http://ics.org.ru/upload/iblock/099/147-interaction-between-kirchhoff-vortices-and-point-vortices-in-an-ideal-fluid_ru.pdf -- 359.3 Кб -- 28.10.2015
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198. http://ics.org.ru/upload/iblock/4e8/148-conservation-laws-hierarchy-of-dynamics-and-explicit-integration-of-nonholonomic-systems-_en.pdf
ISSN 1560-3547, Regular and Chaotic Dynamics, 2008, Vol. 13, No. 5, pp. 443-489. c Pleiades Publishing, Ltd., 2008. NONHOLONOMIC MECHANICS Conservation Laws, Hierarchy of Dynamics and Explicit Integration of Nonholonomic Systems A. V. Borisov* and I. S. Mamaev* * Institute of Computer Science, Udmurt State University, ul. Universitetskaya 1, Izhevsk, 426034 Russia Received April 4, 2008; accepted August 30, 2008 Abstract--This paper can be regarded as a continuation of our previous work [1, 2] on the
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Ссылки http://ics.org.ru/upload/iblock/4e8/148-conservation-laws-hierarchy-of-dynamics-and-explicit-integration-of-nonholonomic-systems-_en.pdf -- 509.2 Кб -- 28.10.2015
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199. http://ics.org.ru/upload/iblock/e2c/146-rolling-of-a-non-homogeneous-ball-over-a-sphere-without-slipping-and-twisting_ru.pdf
ISSN 1560-3547, Regular and Chaotic Dynamics, 2007, Vol. ... RESEARCH ARTICLES Rolling of a Non-Homogeneous Ball over a Sphere Without Slipping and Twisting A. V. Borisov* and I. S. Mamaev ** Institute of Computer Science, Udmurt State University, Universitetskaya ul. ... The integrable cases are found. ... CONSTRAINT REALIZATION AND THE EQUATIONS OF MOTION Consider the problem of rolling a dynamically asymmetric balanced ball (the Chaplygin ball) over the surface of a sphere. ...
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Ссылки http://ics.org.ru/upload/iblock/e2c/146-rolling-of-a-non-homogeneous-ball-over-a-sphere-without-slipping-and-twisting_ru.pdf -- 190.5 Кб -- 28.10.2015
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200. http://ics.org.ru/upload/iblock/e85/145-asymptotic-stability-and-associated-problems-of-dynamics-of-falling-rigid-body_en.pdf
ISSN 1560-3547, Regular and Chaotic Dynamics, 2007, Vol. 12, No. 5, pp. 531-565. c Pleiades Publishing, Ltd., 2007. 150 th ANNIVERSARY OF A. M. LYAPUNOV Asymptotic Stability and Associated Problems of Dynamics of Falling Rigid Body A. V. Borisov1* , V. V. Kozlov 1 2** , and I. S. Mamaev 1 *** 2 Institute of Computer Science, Udmurt State University, ul. ... The equations of motion for the second problem are non-holonomic and exhibit some new features not typical for Hamiltonian systems. ...
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Ссылки http://ics.org.ru/upload/iblock/e85/145-asymptotic-stability-and-associated-problems-of-dynamics-of-falling-rigid-body_en.pdf -- 1856.5 Кб -- 28.10.2015
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