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161. http://ics.org.ru/upload/iblock/119/201-superintegrable-generalizations-of-the-kepler-and-hook-problems_ru.pdf
ISSN 1560-3547, Regular and Chaotic Dynamics, 2014, Vol. ... Their application to the case of p otential forces most naturally leads to sup erintegrable systems with a set of quadratic integrals. ... In [63] (2009) the closedness of the system tra jectories on the plane R2 was shown with a generalization of the p otential (0.3) of the form: b 1 a + , Q. V = 2r2 + 2 2 2 r sin cos An explicit form of the sup erintegral for this system was found in [35]. ... REGULAR AND CHAOTIC DYNAMICS Vol. ... 2 y Vol. ...
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Ссылки http://ics.org.ru/upload/iblock/119/201-superintegrable-generalizations-of-the-kepler-and-hook-problems_ru.pdf -- 301.9 Кб -- 28.10.2015
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162. http://ics.org.ru/upload/iblock/f2a/197-the-reversal-and-chaotic-attractor-in-the-nonholonomic-model-of-chaplygin-s-top_ru.pdf
ISSN 1560-3547, Regular and Chaotic Dynamics, 2014, Vol. ... The Reversal and Chaotic Attractor in the Nonholonomic Mo del of Chaplygin's Top Alexey V. Borisov1* , Alexey O. Kazakov2** , and Igor R. Sataev3 1 Udmurt State University, ul. ... The motion of the ball is governed by the nonholonomic reversible system of 6 differential equations. ... Vol. ... REGULAR AND CHAOTIC DYNAMICS Vol. ... CHAOTIC DYNAMICS We now turn our attention to chaotic dynamics in the nonholonomic model of Chaplygin's top. ...
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Ссылки http://ics.org.ru/upload/iblock/f2a/197-the-reversal-and-chaotic-attractor-in-the-nonholonomic-model-of-chaplygin-s-top_ru.pdf -- 1321.8 Кб -- 28.10.2015
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163. http://ics.org.ru/upload/iblock/d2d/196-the-dynamics-and-control-of-a-spherical-robot-with-an-internal-omniwheel-platform_ru.pdf
ISSN 1560-3547, Regular and Chaotic Dynamics, 2015, Vol. ... The Dynamics and Control of a Spherical Robot with an Internal Omniwheel Platform Yury L. Karavaev1* and Alexander A. Kilin 1 2** M. T. Kalashnikov Izhevsk State Technical University, ul. ... The problem of control of spherical robot motion along an arbitrary tra jectory is solved within the framework of a kinematic mo del and a dynamic mo del. ... To describe the motion of a spherical robot, we consider three coordinate systems. ... Vol. ...
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Ссылки http://ics.org.ru/upload/iblock/d2d/196-the-dynamics-and-control-of-a-spherical-robot-with-an-internal-omniwheel-platform_ru.pdf -- 1417.6 Кб -- 28.10.2015
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164. http://ics.org.ru/upload/iblock/b6d/195-dynamics-and-control-of-an-omniwheel-vehicle_ru.pdf
ISSN 1560-3547, Regular and Chaotic Dynamics, 2015, Vol. ... Dynamics and Control of an Omniwheel Vehicle Alexey V. Borisov1, 2* , Alexander A. Kilin1** , and Ivan S. Mamaev1, 1 3 *** Udmurt State University ul. ... An explicit motion control algorithm for the omniwheel vehicle moving along an arbitrary tra jectory is obtained. ... REGULAR AND CHAOTIC DYNAMICS Vol. ... 2 (4.1) 2015 REGULAR AND CHAOTIC DYNAMICS REGULAR AND CHAOTIC DYNAMICS DYNAMICS AND CONTROL OF AN OMNIWHEEL VEHICLE Vol. ...
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Ссылки http://ics.org.ru/upload/iblock/b6d/195-dynamics-and-control-of-an-omniwheel-vehicle_ru.pdf -- 1138.1 Кб -- 28.10.2015
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165. http://ics.org.ru/upload/iblock/cfe/194-the-dynamics-of-systems-with-servoconstraints-i_ru.pdf
ISSN 1560-3547, Regular and Chaotic Dynamics, 2015, Vol. ... The Dynamics of Systems with Servoconstraints. ... The presence of symmetries allows one to reduce the dynamic equations to a closed system of differential equations with quadratic right-hand sides on a Lie algebra. ... If v (x) = 0 for x = 0, then the system (3.1) admits an invariant straight line x = , where is a nonzero vector from Rp and the parameter changes with time according to the differential equation = c2 , c = 0. ... Theorem 2. ...
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Ссылки http://ics.org.ru/upload/iblock/cfe/194-the-dynamics-of-systems-with-servoconstraints-i_ru.pdf -- 811.8 Кб -- 28.10.2015
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166. http://ics.org.ru/upload/iblock/e5b/193-the-jacobi-integral-in-nonholonomic-mechanics_ru.pdf
ISSN 1560-3547, Regular and Chaotic Dynamics, 2015, Vol. ... The Jacobi Integral in Nonholonomic Mechanics Alexey V. Borisov1, 2* 1 , Ivan. ... Thus, in this case it is necessary to analyze the (complete) system (2.6), which preserves the Jacobi integral. ... 3) 2015 REGULAR AND CHAOTIC DYNAMICS THE JACOBI INTEGRAL IN NONHOLONOMIC MECHANICS 393 In some cases, to describe the motion, it is convenient to use the variables and (see Section 3.2) and in other cases the variables , r (see Section 3.3). ...
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Ссылки http://ics.org.ru/upload/iblock/e5b/193-the-jacobi-integral-in-nonholonomic-mechanics_ru.pdf -- 991.0 Кб -- 28.10.2015
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167. http://ics.org.ru/upload/iblock/4bf/191-the-bifurcation-analysis-and-the-conley-index-in-mechanics_ru.pdf
... Bifurcation Analysis and the Conley Index in Mechanics1 Alexey V. Bolsinov1, 2* , Alexey V. Borisov2** , and Ivan S. Mamaev2 *** 1 School of Mathematics, Loughborough University United Kingdom, LE11 3TU, Loughborough, Leicestershire 2 Institute of Computer Science, Udmurt State University, ul. ... We discuss the phenomenon of appearance (disappearance) of equilibrium points under the change of the Morse index of a critical point of a Hamiltonian. ... Fig. ... 2 REGULAR AND CHAOTIC DYNAMICS Vol. ...
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Ссылки http://ics.org.ru/upload/iblock/4bf/191-the-bifurcation-analysis-and-the-conley-index-in-mechanics_ru.pdf -- 615.3 Кб -- 28.10.2015
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168. http://ics.org.ru/upload/iblock/e3f/192-the-dynamics-of-systems-with-servoconstraints-ii_ru.pdf
... The Dynamics of Systems with Servoconstraints. ... Vakonomic systems are a particular case. ... Servoconstraints can be realized in different ways, and the form of the equations of motion for a controlled mechanical system depends considerably on the method of realization. ... Vol. ... Since the system (6.13) admits the first integral F = (, ), the vector equation (6.13) in the case of the vakonomic model is integrated by quadratures according to the Euler ґ Jacobi theorem of the last multiplier. ...
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Ссылки http://ics.org.ru/upload/iblock/e3f/192-the-dynamics-of-systems-with-servoconstraints-ii_ru.pdf -- 862.9 Кб -- 28.10.2015
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169. http://ics.org.ru/upload/iblock/250/188-an-extended-hamilton-jacobi-method_ru.pdf
... CLEBSCH POTENTIALS In [1] we develop a vortex method for integrating the Hamilton differential equations xk = H , yk yk = - H , xk 1 k n. (1.1) The Hamiltonian H is a smooth function of coordinates x = (x1 ,... ,xn ), momenta y = (y1 ,... ,yn ) and time t. This method involves the search for a complete solution to the system of generalized Lamb's Eqs. (1.2) are a closed nonlinear system of first-order partial differential equations with respect to the functions u1 ,... ,un . ...
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Ссылки http://ics.org.ru/upload/iblock/250/188-an-extended-hamilton-jacobi-method_ru.pdf -- 217.5 Кб -- 28.10.2015
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170. http://ics.org.ru/upload/iblock/8b0/187-the-dynamics-of-vortex-rings-leapfrogging-choreographies-and-the-stability-problem_ru.pdf
ISSN 1560-3547, Regular and Chaotic Dynamics, 2013, Vol. ... MSC2010 numbers: 76B47 DOI: 10.1134/S1560354713010036 Keywords: ideal fluid, vortex ring, leapfrogging motion of vortex rings , bifurcation complex, periodic solution, integrability, chaotic dynamics In memory of H. Aref and V. V. Meleshko Contents INTRODUCTION 1 EQUATIONS OF MOTION FOR VORTEX RINGS 1.1 Axisymmetric Vortex Flows without Swirl 1.2 Toroidal Vortex Rings 1.3 Integrals of ... TWO VORTEX RINGS 2.1. ...
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Ссылки http://ics.org.ru/upload/iblock/8b0/187-the-dynamics-of-vortex-rings-leapfrogging-choreographies-and-the-stability-problem_ru.pdf -- 858.4 Кб -- 28.10.2015
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171. http://ics.org.ru/upload/iblock/704/186-the-self-propulsion-of-a-body-with-moving-internal-masses-in-a-viscous-fluid_ru.pdf
... The Self-propulsion of a Body with Moving Internal Masses in a Viscous Fluid Evgeny V. Vetchanin1* , Ivan S. Mamaev2, 1 3, 4 ** , and Valentin A. Tenenev1 *** Izhevsk State Technical University ul. ... His formula for resistance (drag) force is 1 (1) F = V 2 SCD , 2 where V is the velocity, is the density of the fluid, S is the midsection and CD is the coefficient of resistance. ... Section 2 presents a mathematical model describing the motion of a body with internal masses and a fluid surrounding...
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Ссылки http://ics.org.ru/upload/iblock/704/186-the-self-propulsion-of-a-body-with-moving-internal-masses-in-a-viscous-fluid_ru.pdf -- 1754.9 Кб -- 28.10.2015
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172. http://ics.org.ru/upload/iblock/c34/185-how-to-control-the-chaplygin-ball-using-rotors-ii_en.pdf
... How to Control the Chaplygin Ball Using Rotors. ... In this paper we investigate the controllability of a ball in the presence of friction. ... We parametrize the orientation matrix of the ball Q by the Euler angles: cos cos - cos sin sin cos sin +cos cos sin sin sin Q = - sin cos - cos sin cos - sin sin +cos cos cos cos sin sin sin - sin cos cos , (3.7) where is the nutation angle, is the angle of proper rotation and is the angle of precession. ... We note that in the case of dry friction (i.e. |F ...
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Ссылки http://ics.org.ru/upload/iblock/c34/185-how-to-control-the-chaplygin-ball-using-rotors-ii_en.pdf -- 1774.6 Кб -- 28.10.2015
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173. http://ics.org.ru/upload/iblock/25c/182-topological-analysis-of-an-integrable-system-related-to-the-rolling-of-a-ball-on-a-sphere_ru.pdf
ISSN 1560-3547, Regular and Chaotic Dynamics, 2013, Vol. ... Previously the authors found the separation of variables for this system on the zero level set of a linear (in angular velo city) first integral, whereas in the general case it is not possible to separate the variables. ... EQUATIONS OF MOTION AND FIRST INTEGRALS Consider a system describing the rolling of a rigid b ody whose spherical cavity is in contact with the spherical base (see Fig. ... REGULAR AND CHAOTIC DYNAMICS Vol. ...
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Ссылки http://ics.org.ru/upload/iblock/25c/182-topological-analysis-of-an-integrable-system-related-to-the-rolling-of-a-ball-on-a-sphere_ru.pdf -- 489.4 Кб -- 28.10.2015
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174. http://ics.org.ru/upload/iblock/e9c/178-the-problem-of-drift-and-recurrence-for-the-rolling-chaplygin-ball_en.pdf
ISSN 1560-3547, Regular and Chaotic Dynamics, 2013, Vol. ... MSC2010 numbers: 70E18, 37J60, 70K43, 37J15, 37J20 DOI: 10.1134/S1560354713060166 Keywords: nonholonomic constraint, absolute dynamics , bifurcation diagram, bifurcation complex, drift, resonance, invariant torus Dedicated to Alain Chenciner on the occasion of his 70th birthday, with esteem and admiration Contents INTRODUCTION 1 2 3 EQUATIONS OF MOTION VARIOUS TYPES OF TRAJECTORIES OF A REDUCED SYSTEM AND THE VELOCITY OF THE ... Vol. ...
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Ссылки http://ics.org.ru/upload/iblock/e9c/178-the-problem-of-drift-and-recurrence-for-the-rolling-chaplygin-ball_en.pdf -- 703.9 Кб -- 28.10.2015
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175. http://ics.org.ru/upload/iblock/51b/175-remarks-on-integrable-systems_ru.pdf
... Special attention is paid to linear Hamiltonian systems. The paper discusses the general problem of integrability of the systems of autonomous differential equations in an n-dimensional space, which admit the algebra of symmetry fields of dimension n. Using a metho d due to Liouville, this problem is reduced to investigating the integrability conditions for Hamiltonian systems with Hamiltonians linear in the momenta in phase space of dimension that is twice as large. ... Theorem 1. ...
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Ссылки http://ics.org.ru/upload/iblock/51b/175-remarks-on-integrable-systems_ru.pdf -- 187.8 Кб -- 28.10.2015
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176. http://ics.org.ru/upload/iblock/702/176-the-dynamics-of-a-rigid-body-with-a-sharp-edge-in-contact-with-an-inclined-surface-in-the-presence-o_ru.pdf
... MSC2010 numbers: 70F40, 70E18 DOI: 10.1134/S1560354714010080 Keywords: ro d, PainlevЄ paradox, dry friction, loss of contact , frictional impact e Contents 1 2 INTRODUCTION MAT 2.1 2.2 2.3 2.4 HEMATICAL MODELS DESCRIBING VARIOUS TYPES OF MOTION An Inverted Pendulum A Sliding Rod A Free Rod Problems of Consistent Change of Motion Regimes 117 118 119 120 121 121 123 123 124 124 127 127 132 132 136 3 THE BOUNDARIES OF ... Sliding ro d ґ free system. ... Inverted p endulum ґ free system. ...
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Ссылки http://ics.org.ru/upload/iblock/702/176-the-dynamics-of-a-rigid-body-with-a-sharp-edge-in-contact-with-an-inclined-surface-in-the-presence-o_ru.pdf -- 736.7 Кб -- 28.10.2015
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177. http://ics.org.ru/upload/iblock/3e6/174-the-dynamics-of-nonholonomic-systems-consisting-of-a-spherical-shell-with-a-moving-rigid-body-inside_ru.pdf
ISSN 1560-3547, Regular and Chaotic Dynamics, 2014, Vol. ... The Dynamics of Nonholonomic Systems Consisting of a Spherical Shell with a Moving Rigid Bo dy Inside Ivan A. Bizyaev1* , Alexey V. Borisov2** , and Ivan S. Mamaev1 Udmurt State University, ul. ... We show an isomorphism between the equations of motion for the inner body with those for the ball moving on a smo oth plane. ... Equations of motion for this system have been obtained and new integrable cases found. ... Equations of motion. ...
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Ссылки http://ics.org.ru/upload/iblock/3e6/174-the-dynamics-of-nonholonomic-systems-consisting-of-a-spherical-shell-with-a-moving-rigid-body-inside_ru.pdf -- 242.5 Кб -- 28.10.2015
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178. http://ics.org.ru/upload/iblock/ca2/173-hamiltonicity-and-integrability-of-the-suslov-problem_ru.pdf
... In this case, the equations of the constraint has the form 3 = 0, (1.2) and the equations of motion that describ e the variations in the angular velocity with the constraint taken into account assume the form I11 1 = -2 (I13 1 + I23 2 )+ M1 , I22 2 = 1 (I13 1 + I23 2 )+ M2 , I13 1 + I23 2 = (I11 - I22 )1 2 + + M3 , (1.3) where Mi is the comp onent of the moment of the external forces and is the Lagrange undetermined multiplier. ... 1 = 2 2I , 2 I13 I22 + I23 11 I13 I22 + I23 I11 Remark 2. ...
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Ссылки http://ics.org.ru/upload/iblock/ca2/173-hamiltonicity-and-integrability-of-the-suslov-problem_ru.pdf -- 240.8 Кб -- 28.10.2015
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179. http://ics.org.ru/upload/iblock/400/172-hamiltonization-of-nonholonomic-systems-in-the-neighborhood-of-invariant-manifolds_ru.pdf
... The first part of the paper is devoted to representing integrable systems in a conformally Hamiltonian form. ... MSC2010 numbers: 37Jxx DOI: 10.1134/S1560354711050030 Keywords: conformally Hamiltonian system , non-holonomic system , invariant measure , periodic tra jectory, invariant torus, integrable system Contents INTRODUCTION 1 HAMILTONIZATION IN A NEIGHBORHOOD OF A TWO-DIMENSIONAL INVARIANT MANIFOLD 1.1 Theorem on Rectification of a Vector ... Let us find the vector field J dH ....
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Ссылки http://ics.org.ru/upload/iblock/400/172-hamiltonization-of-nonholonomic-systems-in-the-neighborhood-of-invariant-manifolds_ru.pdf -- 426.8 Кб -- 28.10.2015
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180. http://ics.org.ru/upload/iblock/10f/171-rolling-of-a-homogeneous-ball-over-a-dynamically-asymmetric-sphere_ru.pdf
... Rolling of a Homogeneous Ball over a Dynamically Asymmetric Sphere Alexey V. Borisov* , Alexander A. Kilin** , and Ivan S. Mamaev* Institute of Computer Science, Udmurt State University ul. Universitetskaya 1, Izhevsk 426034, Russia Received Novemb er 11, 2010; accepted Decemb er 6, 2010 ** Abstract--We consider a novel mechanical system consisting of two spherical bodies rolling over each other, which is a natural extension of the famous Chaplygin problem of rolling motion of a ball on a plane. ...
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Ссылки http://ics.org.ru/upload/iblock/10f/171-rolling-of-a-homogeneous-ball-over-a-dynamically-asymmetric-sphere_ru.pdf -- 644.2 Кб -- 28.10.2015
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