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Vol. 5, No. 1

Vol. 5, No. 1, 2009
On the 80th anniversary of Jürgen Mosers's birth

Abstract
Citation: Обращение к коллективу авторов (англ.), On the 80th anniversary of Jürgen Mosers's birth, Rus. J. Nonlin. Dyn., 2009, Vol. 5, No. 1, pp. 3
DOI:10.20537/nd0901001
Abstract
Citation: J.K. Moser. Curriculum Vitae and Bibliography, Rus. J. Nonlin. Dyn., 2009, Vol. 5, No. 1, pp. 5-10
DOI:10.20537/nd0901002
Abstract
Citation: J.Moser works available in Russian, Rus. J. Nonlin. Dyn., 2009, Vol. 5, No. 1, pp. 11-12
DOI:10.20537/nd0901003
Moser J.
Abstract
Citation: Moser J., Dynamical systems — Past and present, Rus. J. Nonlin. Dyn., 2009, Vol. 5, No. 1, pp. 13-32
DOI:10.20537/nd0901004
Adler M.
Abstract
Citation: Adler M., Remembering Jürgen Moser, Rus. J. Nonlin. Dyn., 2009, Vol. 5, No. 1, pp. 33-34
DOI:10.20537/nd0901005
Belbruno E.
Abstract
Citation: Belbruno E., Recollections of Jürgen Moser, Rus. J. Nonlin. Dyn., 2009, Vol. 5, No. 1, pp. 35-36
DOI:10.20537/nd0901006
Chierchia L.
Abstract
Citation: Chierchia L., Meeting Jürgen Moser, Rus. J. Nonlin. Dyn., 2009, Vol. 5, No. 1, pp. 37-38
DOI:10.20537/nd0901007
Veselov A. P.
Abstract
Citation: Veselov A. P., A Few Things I Learnt from Jьrgen Moser, Rus. J. Nonlin. Dyn., 2009, Vol. 5, No. 1, pp. 39-51
DOI:10.20537/nd0901008
Borisov A. V.,  Kilin A. A.,  Mamaev I. S.
Abstract
Systems of material points interacting both with one another and with an external field are considered in Euclidean space. For the case of arbitrary binary interaction depending solely on the mutual distance between the bodies, new integrals are found, which form a Galilean momentum vector.

A corresponding algebra of integrals constituted by the integrals of momentum, angular momentum, and Galilean momentum is presented. Particle systems with a particle-interaction potential homogeneous of degree $α=-2$ are considered. The most general form of the additional integral of motion, which we term the Jacobi integral, is presented for such systems. A new nonlinear algebra of integrals including the Jacobi integral is found. A systematic description is given to a new reduction procedure and possibilities of applying it to dynamics with the aim of lowering the order of Hamiltonian systems.

Some new integrable and superintegrable systems generalizing the classical ones are also described. Certain generalizations of the Lagrangian identity for systems with a particle-interaction potential homogeneous of degree $α=-2$ are presented. In addition, computational experiments are used to prove the nonintegrability of the Jacobi problem on a plane.
Keywords: multiparticle systems, Jacobi integral
Citation: Borisov A. V.,  Kilin A. A.,  Mamaev I. S., Multiparticle Systems. The Algebra of Integrals and Integrable Cases, Rus. J. Nonlin. Dyn., 2009, Vol. 5, No. 1, pp. 53-82
DOI:10.20537/nd0901009
Kilin A. A.
Abstract
3-particle systems with a particle-interaction homogeneous potential of degree $α=-2$ is considered. A constructive procedure of reduction of the system by 2 degrees of freedom is performed. The nonintegrability of the systems is shown using the Poincare mapping.
Keywords: multiparticle system, potential, Hamiltonian, reduction, integrability
Citation: Kilin A. A., The Jacobi problem on a plane, Rus. J. Nonlin. Dyn., 2009, Vol. 5, No. 1, pp. 83-86
DOI:10.20537/nd0901010
Markeev A. P.
Abstract
The motion of a rigid body about its center of mass under action of gravitational moments of the central Newtonian force field is investigated. The orbit of the center of mass is proposed to be an elliptical one, the eccentricity of the orbit is equal to the one of the Mercury. The central ellipsoid of inertia of the body is arbitrary. The problem of existence of planar periodical rotations under resonance 3:2 of the Mercurian type is considered and their stability (in Liapunov) is investigated. In a case of planar perturbations the nonlinear problem of stability is solved. In a case of arbitrary perturbations of periodical rotations the stability in first (linear) approximation is investigated.
Keywords: Mercury, resonance, periodic motion, stability
Citation: Markeev A. P., To the theory of Resonant Rotation of the Mercury, Rus. J. Nonlin. Dyn., 2009, Vol. 5, No. 1, pp. 87-98
DOI:10.20537/nd0901011
Akulenko L. D.,  Georgievsky D. V.,  Nesterov S. V.
Abstract
Citation: Akulenko L. D.,  Georgievsky D. V.,  Nesterov S. V., Preface to the translations of two classic works of Jeffery and Hamel, Rus. J. Nonlin. Dyn., 2009, Vol. 5, No. 1, pp. 99-100
DOI:10.20537/nd0901012
Jeffery G. B.
Abstract
Citation: Jeffery G. B., The Two-Dimensional Steady Motion of a Viscous Fluid, Rus. J. Nonlin. Dyn., 2009, Vol. 5, No. 1, pp. 101-109
DOI:10.20537/nd0901013
Hamel G.
Abstract
Citation: Hamel G., Spiral Motions of Viscous Fluids, Rus. J. Nonlin. Dyn., 2009, Vol. 5, No. 1, pp. 111-133
DOI:10.20537/nd0901014
Abstract
Citation: G. B. Jeffery and G. Hamel. Brief Biographies, Rus. J. Nonlin. Dyn., 2009, Vol. 5, No. 1, pp. 135-136
DOI:10.20537/nd0901015
Abstract
Citation: New books of the Scientific and Publishing Center «Regular and Chaotic Dynamics» and Institute of Computer Science (Moscow-Izhevsk), Rus. J. Nonlin. Dyn., 2009, Vol. 5, No. 1, pp. 137-139

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