Classical integrable mechanical systems and their integrable perturbations.

Dragović, Vladimir

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Displaying similar documents to “Classical integrable mechanical systems and their integrable perturbations.”

Algebro-geometric Integration in Classical and Statistical Mechanics

Vladimir Dragovic (2006)

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On the KAM - Theory Conditions for the Kirchhoff Top

Christov, Ognyan (1997)

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* Partially supported by Grant MM523/95 with Ministry of Science and Technologies. In this paper the classical Kirchhoff case of motion of a rigid body in an infinite ideal fluid is considered. Then for the corresponding Hamiltonian system on the zero integral level, the KAM theory conditions are checked. In contrast to the known similar results, there exists a curve in the bifurcation diagram along which the Kolmogorov’s condition vanishes for certain values of the parameters. ...

A new hierarchy of integrable system of $1 + 2$ dimensions: from Newton's law to generalized Hamiltonian system. II.

Huang, Xuncheng, Tu, Guizhang (2006)

International Journal of Mathematics and Mathematical Sciences

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Non-integrability of certain Hamiltonian systems. Applications of the Morales-Ramis differential Galois extension of Ziglin theory

Andrzej J. Maciejewski (2002)

Banach Center Publications

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The aim of this paper is to present two examples of non academic Hamiltonian systems for which the Morales-Ramis theory can be applied effectively. First, we investigate the Gross-Neveu system with n degrees of freedom. Till now it has been proved that this system is not integrable for n = 3. We give a simple proof that it is not completely integrable for an arbitrary n ≥ 3. Our second example is a natural generalisation of the Jacobi problem of a material point moving on an ellipsoid....

Perturbations of Systems Describing the Motion of a Particle in Central Fields

Christov, Ognyan, Dragnev, Dragomir (1995)

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The present paper deals with the KAM-theory conditions for systems describing the motion of a particle in central field.

Chaotic behaviour in the solar system

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Integration of the perturbated Jacobi problem.

Dragović, Vladimir (1998)

Publications de l'Institut Mathématique. Nouvelle Série

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Completely integrable class of mechanical systems connected with Korteweg-de Vries and multicomponent Schrödinger equations - I

D. V. Choodnovsky, G. V. Choodnovsky (1977-1978)

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The Lagrange rigid body motion

Tudor Ratiu, P. van Moerbeke (1982)

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We discuss the motion of the three-dimensional rigid body about a fixed point under the influence of gravity, more specifically from the point of view of its symplectic structures and its constants of the motion. An obvious symmetry reduces the problem to a Hamiltonian flow on a four-dimensional submanifold of $s o (3) \times s o (3)$ ; they are the customary Euler-Poisson equations. This symplectic manifold can also be regarded as a coadjoint orbit of the Lie algebra of the semi-direct product group $S O (3) \times s o (3)$ with...

Symmetries and Integrability

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On the Isoenergetical Non-Degeneracy of the Problem of two Centers of Gravitation

Dragnev, Dragomir (1997)

Serdica Mathematical Journal

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* Partialy supported by contract MM 523/95 with Ministry of Science and Technologies of Republic of Bulgaria. For the system describing the motion of a moss point under the action of two static gravity centers (with equal masses), we find a subset of the set of the regular values of the energy and momentum, where the condition of isoenergetical non-degeneracy is fulfilled.