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201. http://ics.org.ru/upload/iblock/ac0/144-on-the-problem-of-motion-of-vortex-sources-on-a-plane-_ru.pdf
... Izhevsk 426034, Russia E-mails: b orisov@ics.org.ru, mamaev@ics.org.ru ON THE PROBLEM OF MOTION VORTEX SOURCES ON A PLANE Received September 05, 2005; accepted March 07, 2006 DOI: 10.1070/RD2006v011n04ABEH000363 Equations of motion of vortex sources (examined earlier by Fridman and Polubarinova) are studied, and the problems of their being Hamiltonian and integrable are discussed. A system of two vortex sources and three sources-sinks was examined. ... Three-vortex system 5.1. ...
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Ссылки http://ics.org.ru/upload/iblock/ac0/144-on-the-problem-of-motion-of-vortex-sources-on-a-plane-_ru.pdf -- 378.5 Кб -- 28.10.2015
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202. http://ics.org.ru/upload/iblock/261/143-superintegrable-systems-on-a-sphere-_ru.pdf
... 426034 Izhevsk, Russia E-mail: b orisov@rcd.ru, mamaev@rcd.ru SUPERINTEGRABLE SYSTEMS ON A SPHERE Received October 25, 2004; accepted February 15, 2005 DOI: 10.1070/RD2005v010n03ABEH000314 We consider various generalizations of the Kepler problem to three-dimensional sphere S 3 (a compact space of constant curvature). ... The e mentioned systems are integrable superintegrable, and there exists the vector integral which is analogous to the Laplace ґ Runge ґ Lenz vector. ... The Kepler problem in R3 ....
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Ссылки http://ics.org.ru/upload/iblock/261/143-superintegrable-systems-on-a-sphere-_ru.pdf -- 313.8 Кб -- 28.10.2015
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203. http://ics.org.ru/upload/iblock/daa/139-notes-on-diffusion-in-collisionless-medium_ru.pdf
V. V. KOZLOV Steklov Institute of Mathematics Russian Academy of Sciences 117966 Moscow, Russia E-mail: kozlov@pran.ru NOTES ON DIFFUSION IN COLLISIONLESS MEDIUM Received October 06, 2003 DOI: 10.1070/RD2004v009n01ABEH000262 A collisionless continuous medium in Euclidean space is discussed, i. e. a continuum of free particles moving inertially, without interacting with each other. It is shown that the distribution density of such medium is weakly converging to zero as time increases indefinitely. ...
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Ссылки http://ics.org.ru/upload/iblock/daa/139-notes-on-diffusion-in-collisionless-medium_ru.pdf -- 150.0 Кб -- 28.10.2015
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204. http://ics.org.ru/upload/iblock/c59/137-billiards-invariant-measures-and-equilibrium-thermodynamics-ii_ru.pdf
... We have assumed that in statistical equilibrium, the probability distribution density depends only on the total energy. ... As it is shown in Refs. [1, 2], in a billiards, the probability distribution density as a function of time t (this function satisfies the classic Liouville equation) necessarily has the weak limit as t ?. ... The crucial idea of our approach is : transition to thermo dynamical (statistical) equilibrium is equal to replacement of the distribution (12) with its weak limit. ...
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Ссылки http://ics.org.ru/upload/iblock/c59/137-billiards-invariant-measures-and-equilibrium-thermodynamics-ii_ru.pdf -- 284.7 Кб -- 28.10.2015
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205. http://ics.org.ru/upload/iblock/f96/138-absolute-and-relative-choreographies-in-the-problem-of-point-vortices-moving-on-a-plane_ru.pdf
... 426034, Izhevsk, Russia E-mail: b orisov@rcd.ru E-mail: mamaev@rcd.ru E-mail: aka@rcd.ru ABSOLUTE AND RELATIVE CHOREOGRAPHIES IN THE PROBLEM OF POINT VORTICES MOVING ON A PLANE Received April 05, 2004 DOI: 10.1070/RD2004v009n02ABEH000269 We obtained new periodic solutions in the problems of three and four point vortices moving on a plane. ... Figure 3 shows the relative choreographies that corresp ond to the new p erio dic solution of the reduced system (10). ... I ґ The case of identical vortices. ...
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Ссылки http://ics.org.ru/upload/iblock/f96/138-absolute-and-relative-choreographies-in-the-problem-of-point-vortices-moving-on-a-plane_ru.pdf -- 390.1 Кб -- 28.10.2015
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206. http://ics.org.ru/upload/iblock/b6b/134-generalization-of-the-goryachev-ndash-chaplygin-case_ru.pdf
of Dynamical Chaos and Nonlinearity Udmurt State University, Universitetskaya, 1 426034, Izhevsk, Russia E-mail: mamaev@rcd.ru GENERALIZATION OF THE GORYACHEV ґ CHAPLYGIN CASE Received December 20, 2001 DOI: 10.1070/RD2002v007n01ABEH000192 In this paper we present a generalization of the Goryachev ґ Chaplygin integrable case on a bundle of Poisson brackets, and on Sokolov terms in his new integrable case of Kirchhoff ... In this case integral (33) has the form F1 = m 3 + m 4 . ...
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Ссылки http://ics.org.ru/upload/iblock/b6b/134-generalization-of-the-goryachev-ndash-chaplygin-case_ru.pdf -- 290.2 Кб -- 28.10.2015
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207. http://ics.org.ru/upload/iblock/daf/135-on-justification-of-gibbs-distribution_ru.pdf
V. V. KOZLOV Department of Mechanics and Mathematics Moscow State University, Vorob'ievy Gory 119899, Moscow, Russia ON JUSTIFICATION OF GIBBS DISTRIBUTION Received January 10, 2001 DOI: 10.1070/RD2002v007n01ABEH000190 The paper develop a new approach to the justification of Gibbs canonical distribution for Hamiltonian systems with finite number of degrees of freedom. It uses the condition of nonintegrability of the ensemble of weak interacting Hamiltonian systems. ... Energy h is non-negative. ...
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Ссылки http://ics.org.ru/upload/iblock/daf/135-on-justification-of-gibbs-distribution_ru.pdf -- 325.3 Кб -- 28.10.2015
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208. http://ics.org.ru/upload/iblock/703/132-the-rolling-motion-of-a-ball-on-a-surface-new-integrals-and-hierarchy-of-dynamics_ru.pdf
... Motion of a ball on a cylindrical surface . ... The rolling of a ball on a surface surface typ e measure additional integrals Hamiltonianity cylindrical surface measure exists system is integrable by quadratures surface of the second order ellipsoid, hyp erb oloid, cone of the second order parab oloid = ( , B ) -1 -2 surface of revolution arbitrary surface ellipsoid, hyp erb oloid = (f ( 3 )) 3 parab oloid, cone, cylinder f ( 3 ) - sphere = (B -1 rc , B -1 rc ) -1 1 2 - 3 3 f ( 3...
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Ссылки http://ics.org.ru/upload/iblock/703/132-the-rolling-motion-of-a-ball-on-a-surface-new-integrals-and-hierarchy-of-dynamics_ru.pdf -- 629.3 Кб -- 28.10.2015
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209. http://ics.org.ru/upload/iblock/b91/131-on-the-integration-theory-of-equations-of-nonholonomic-mechanics_ru.pdf
V. V. KOZLOV Department of Mechanics and Mathematics Moscow State University, Vorob'ievy Gory 119899, Moscow, Russia ON THE INTEGRATION THEORY OF EQUATIONS OF NONHOLONOMIC MECHANICS * DOI: 10.1070/RD2002v007n02ABEH000203 The paper deals with the problem of integration of equations of motion in nonholonomic systems. By means of well-known theory of the differential equations with an invariant measure the new integrable systems are discovered. ... It is not so in the case of nonholonomic systems. ...
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Ссылки http://ics.org.ru/upload/iblock/b91/131-on-the-integration-theory-of-equations-of-nonholonomic-mechanics_ru.pdf -- 457.4 Кб -- 28.10.2015
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210. http://ics.org.ru/upload/iblock/3a8/128-dynamics-of-rolling-disk_ru.pdf
A. V. BORISOV, I. S. MAMAEV, A. A. KILIN Institute of Computer Science Universitetskaya, 1 426034, Izhevsk, Russia E-mail: b orisov@rcd.ru E-mail: mamaev@rcd.ru E-mail: aka@rcd.ru DYNAMICS OF ROLLING DISK Received August 22, 2002 DOI: 10.1070/RD2003v008n02ABEH000237 In the paper we present the qualitative analysis of rolling motion without slipping of a homogeneous round disk on a horisontal plane. ... Let's consider a motion of the p oint of contact on a plane. ... Regular and Chaotic Dynamics. ...
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Ссылки http://ics.org.ru/upload/iblock/3a8/128-dynamics-of-rolling-disk_ru.pdf -- 649.4 Кб -- 28.10.2015
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211. http://ics.org.ru/upload/iblock/c44/129-an-integrability-of-the-problem-on-motion-of-cylinder-and-vortex-in-the-ideal-fluid_ru.pdf
... Integrability of the Problem of the Motion of a Cylinder and a Vortex in an Ideal Fluid A. V. Borisov and I. S. Mamaev Received July 4, 2002 Abstract--In this paper, we obtain a nonlinear Poisson structure and two first integrals in the problem of the plane motion of a circular cylinder and n point vortices in an ideal fluid. ... 1 2004 (4) MATHEMATICAL NOTES MOTION OF A CYLINDER AND A VORTEX IN AN IDEAL FLUID 21 generating (by the structure (3)) the symmetry field vF = 2(v2 , -v1 ,y , -x). ... 1...
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Ссылки http://ics.org.ru/upload/iblock/c44/129-an-integrability-of-the-problem-on-motion-of-cylinder-and-vortex-in-the-ideal-fluid_ru.pdf -- 91.4 Кб -- 28.10.2015
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212. http://ics.org.ru/upload/iblock/64e/127-new-cases-when-the-invariant-measure-and-first-integrals-exist-in-the-problem-of-a-body-rolling-on-a_ru.pdf
I. S. MAMAEV Institute of computer science 426034, Russia, Izhevsk Universitetskaya St., 1 E-mail: mamaev@rcd.ru NEW CASES WHEN THE INVARIANT MEASURE AND FIRST INTEGRALS EXIST IN THE PROBLEM OF A BODY ROLLING ON A SURFACE Received September 16, 2003 DOI: 10.1070/RD2003v008n03ABEH000249 Some new cases when the invariant measure and an additional first integral exist in the problem of a rigid body rolling on a sphere and on an ellipsoid are discussed in the paper. ... Rolling of a ball on a surface. ...
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Ссылки http://ics.org.ru/upload/iblock/64e/127-new-cases-when-the-invariant-measure-and-first-integrals-exist-in-the-problem-of-a-body-rolling-on-a_ru.pdf -- 149.4 Кб -- 28.10.2015
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213. http://ics.org.ru/upload/iblock/ab8/125-motion-of-a-circular-cylinder-and-n-point-vortices-in-a-perfect-fluid_ru.pdf
Universitetskaya, 1 426034, Izhevsk, Russia E-mail: mamaev@ics.org.ru S. M. RAMODANOV Moscow, Russia E-mail: ramo danov@mail.ru MOTION OF A CIRCULAR CYLINDER AND n POINT VORTICES IN A PERFECT FLUID Received October 29, 2003 DOI: 10.1070/RD2003v008n04ABEH000257 The pap er studies the system of a rigid b ody interacting dynamically with p oint vortices in a p erfect fluid ... The reduced system (5.2) describ es the motion of the vortices relative to the center of the cylinder. ...
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Ссылки http://ics.org.ru/upload/iblock/ab8/125-motion-of-a-circular-cylinder-and-n-point-vortices-in-a-perfect-fluid_ru.pdf -- 586.4 Кб -- 28.10.2015
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214. http://ics.org.ru/upload/iblock/d40/126-galton-board_ru.pdf
... MITROFANOVA E-mail: mitrofanov@breitmeier.de GALTON BOARD Received October 1, 2003 DOI: 10.1070/RD2003v008n04ABEH000255 In this paper, we present results of simulations of a model of the Galton board for various degrees of elasticity of the ball-to-nail collision. ... The funnel is lo cated precisely ab ove the central nail of the second row, i. e. the ball, if p erfectly centered, would fall vertically and directly onto the upp ermost p oint of this nail's surface (Fig. ... Fig. ... MITROFANOVA Fig...
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Ссылки http://ics.org.ru/upload/iblock/d40/126-galton-board_ru.pdf -- 2035.7 Кб -- 28.10.2015
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215. http://ics.org.ru/upload/iblock/a5c/124-kovalevskaya-top-and-generalizations-of-integrable-systems_ru.pdf
... H% d v? P B F C$ A !Е wЕ W$ C? BBA h?g ?Е " #R H f? 3 S% FQ % #? ... BЕ BA XBU 2 X? o Iq !h ko #p #p `p Io n h i ml kj Ii h V? iu r ts Er ? ... Е " #R H 3+ q? Y{ a XЕ 7U 3 ©% H$ @ B s © C? #BY BhA C% ? ... b? #R H E% PIQ f? ( R () H ?? ... W$ C? BBA hCg ( u% W$ C? #FY IQ e !Y !) ... hn · ? 5 ( 5 © · ? ') & B ' ' & A '6 & @9 54 · n ' R 10 ? ?5 n ? ?5 n 20 T ') & ' 8& 76 & 54 · R ? ' n o 5 ( 3 hn 5 n 3 ` n 5 ? 5 © 20 ?5 5 hn n · ') & $ ' j % #" # q ' · ' n j A ?Е " #R H f? XIЕ ?" ...
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Ссылки http://ics.org.ru/upload/iblock/a5c/124-kovalevskaya-top-and-generalizations-of-integrable-systems_ru.pdf -- 287.7 Кб -- 28.10.2015
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216. http://ics.org.ru/upload/iblock/a91/123-first-integral-in-the-problem-of-motion-of-a-circular-cylinder-and-a-point-vortex-in-unbounded-ideal_ru.pdf
... T t V R j t )gw X vu 6 ?b ?2 f Q 'S R!ё ?QP ?є ?? R t u s e ? dt1 sr 0c q 1 EB ё ?? ? A? ?? ?? rі ? 1? Yі n? ? 3ї 3і B? ? є Fё ? h? a h H a a ?ў ? ? Rн 9 GЄ ? t? tи 0и Ёд cA ?Є q ?н ?y HE Vy н 4P ... ё !Ы YЫ БЭ ГЫ 1? 8є E 8є #В В ? vЫ ?% ёШ vі ?? H? ? ? ? #Ы $? Iє ) ? ?? 8& G ё s } } s Hp } } s )Э ?Ы YЬ DВ )Ы Y| YШ В ё 5Ы 5В ( 8& #@ ?Ы ёR P ё? ё R ёё P ёё x R P ёє ё x ё R P } ?ёёё ё x ?% GШ )Э #d 5Ы В ? ? ?Ы YЬ В ё )? Ш ё x ?? 5Ы 5В ( ъ? ё )? Ш ?Ы ) ? s? )В ?є 3? ) r? )Ы ?d )? sШ GЬ C! ) ? Ь H? 8 H...
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Ссылки http://ics.org.ru/upload/iblock/a91/123-first-integral-in-the-problem-of-motion-of-a-circular-cylinder-and-a-point-vortex-in-unbounded-ideal_ru.pdf -- 140.8 Кб -- 28.10.2015
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217. http://ics.org.ru/upload/iblock/650/122-kinetics-of-collisionless-continuous-medium_ru.pdf
V. V. KOZLOV Department of Mechanics and Mathematics Moscow State University, Vorob'ievy Gory 119899, Moscow, Russia E-mail: vako@mech.math.msu.su KINETICS OF COLLISIONLESS CONTINUOUS MEDIUM Received June 8, 2001 DOI: 10.1070/RD2001v006n03ABEH000175 In this article we develop PoincarЄ ideas about a heat balance of ideal gas considered as a collisionless continuous medium. e We obtain the theorems on diffusion in nondegenerate completely integrable systems. ... d3 2 2 For the Maxwell distribution = 1. ...
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Ссылки http://ics.org.ru/upload/iblock/650/122-kinetics-of-collisionless-continuous-medium_ru.pdf -- 469.7 Кб -- 28.10.2015
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218. http://ics.org.ru/upload/iblock/31e/120-the-dynamics-of-chaplygin-ball-the-qualitative-and-computer-analysis_ru.pdf
A. A. KILIN Lab oratory of Dynamical Chaos and Nonlinearity Udmurt State University, Universitetskaya, 1 426034, Izhevsk, Russia E-mail: aka@uni.udm.ru THE DYNAMICS OF CHAPLYGIN BALL: THE QUALITATIVE AND COMPUTER ANALYSIS Received June 3, 2001 DOI: 10.1070/RD2001v006n03ABEH000178 The motion of Chaplygin ball with and without gyroscope in the absolute space is analyzed. In particular, the tra jectories of the point of contact are studied in detail. ... Let us return to the case when C = (M , ) = 0. ...
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Ссылки http://ics.org.ru/upload/iblock/31e/120-the-dynamics-of-chaplygin-ball-the-qualitative-and-computer-analysis_ru.pdf -- 1188.3 Кб -- 28.10.2015
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219. http://ics.org.ru/upload/iblock/38e/121-euler-poisson-equations-and-integrable-cases_ru.pdf
Dynamical Chaos and Nonlinearity Udmurt State University, Universitetskaya, 1 426034, Izhevsk, Russia E-mail: mamaev@rcd.ru EULER ґ POISSON EQUATIONS AND INTEGRABLE CASES Received April 18, 2001 DOI: 10.1070/RD2001v006n03ABEH000176 In this paper we propose a new approach to the We make a new investigation of Kovalevskaya and Goryachev ґ Chaplygin cases of Euler ґ Poisson equations and obtain many new results in rigid body dynamics in absolute space. ... Fig. ... Bobylev ґ Stekloff solution. ...
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Ссылки http://ics.org.ru/upload/iblock/38e/121-euler-poisson-equations-and-integrable-cases_ru.pdf -- 1440.8 Кб -- 28.10.2015
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220. http://ics.org.ru/upload/iblock/970/119-some-comments-to-the-paper-by-a-m-perelomov-quot-a-note-on-geodesics-on-ellipsoid-quot-rcd-2000-5-1-_ru.pdf
A. M. PERELOMOV SOME COMMENTS TO THE PAPER A. V. BORISOV I. S. MAMAEV Department of Theoretical Mechanics MoscowStateUniversity,Vorob'ievy gory 119899 Moscow, Russia E-mail: borisov@uni.udm.ru Laboratory of Dynamical Chaos and Nonlinearity Udmurt State University Universitetskaya 1, 426034 Izhevsk, Russia E-mail: mamaev@uni.udm.ru between the geodesic ow on two-dimensional ellipsoid and a Hamiltonian system on algebra e(3) in the Clebsch case was rst indicated in 3]. ...
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Ссылки http://ics.org.ru/upload/iblock/970/119-some-comments-to-the-paper-by-a-m-perelomov-quot-a-note-on-geodesics-on-ellipsoid-quot-rcd-2000-5-1-_ru.pdf -- 179.4 Кб -- 28.10.2015
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