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1
Content available remote Symplectic singularities and solvable Hamiltonian mappings
Fukuda T., Janeczko S.
Demonstratio Mathematica
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2015
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Vol. 48, nr 2
118--146
EN
We study singularities of smooth mappings (…) of R2n into symplectic space (…) by their isotropic liftings to the corresponding symplectic tangent bundle (…). Using the notion of local solvability of lifting as a generalized Hamiltonian system, we introduce new symplectic invariants and explain their geometric meaning. We prove that a basic local algebra of singularity is a space of generating functions of solvable isotropic mappings over (…) endowed with a natural Poisson structure. The global properties of this Poisson algebra of the singularity among the space of all generating functions of isotropic liftings are investigated. The solvability criterion of generalized Hamiltonian systems is a strong method for various geometric and algebraic investigations in a symplectic space. We illustrate this by explicit classification of solvable systems in codimension one.
2
Content available Buckling of cylindrical shells under external pressure in a Hamiltonian system
Sun J., Xu X., Lim C. W.
Journal of Theoretical and Applied Mechanics
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2014
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Vol. 52 nr 3
641--653
EN
In this article, the elastic buckling behavior of cylindrical shells under external pressure is studied by using a symplectic method. Based on Donnell’s shell theory, the governing equations which are expressed in stress function and radial displacement are re-arranged into the Hamiltonian canonical equations. The critical loads and buckling modes are reduced to solving for symplectic eigenvalues and eigenvectors. The buckling solutions are mainly grouped into four categories according to the natures of the buckling modes. The effects of geometrical parameters and boundary conditions on the buckling loads and modes are examined in detail.
3
Content available Combined algorithm for finding conservation laws and implectic operators for the Boussinesq-Burgers nonlinear dynamical system and its finite dimensional reductions
Kindybaliuk A., Prytula M.
Journal of Applied Mathematics and Computational Mechanics
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2014
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Vol. 13, nr 3
85--99
EN
In the article the combined algorithm for finding conservation laws and implectic operators has been proposed. Using the Novikov-Bogoyavlensky method the finite dimensional reductions have been found. The structure of invariant submanifolds has been examined. Having analyzed phase portraits of Hamiltonian systems, partial periodical solutions have been found.
4
Content available remote On the multiplicity of periodic solutions of an Hamiltonian system
Timouni M.
Demonstratio Mathematica
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2002
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Vol. 35, nr 4
899-913
EN
In this note, we are interested in the existence of multiple periodic solutions of nonautonomous Hamiltonian systems with bounded gradient of the type: Jx+-H'(t,x)+e(t) =0.
5
Content available remote On existence of subharmonic orbits in perturbed Hamiltonian systems
Yang X.
Bulletin of the Polish Academy of Sciences. Mathematics
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2000
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Vol. 48, no 2
221-225
EN
In this paper the existence of subharmonic orbits in planar Hamiltonian system x = f(x) + [epsilon]g(x,t) is revisited. The existing error in treatment on this problem is discussed and a new rigorous treatment is given.
6
Content available remote Closed orbits for a class of Hamiltonian systems
Timouni M.
Demonstratio Mathematica
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1998
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Vol. 31, nr 1
1-10
EN
In this paper we prove the
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