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Symmetry Preserving Discretization of the Hamiltonian Systems with Holonomic Constraints

Mathematics, 2021
Symmetry preserving difference schemes approximating equations of Hamiltonian systems are presented in this paper. For holonomic systems in the Hamiltonian framework, the symmetrical operators are obtained by solving the determining equations of Lie ...
Lili Xia, Mengmeng Wu, Xinsheng Ge
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Ergodicity in Hamiltonian Systems [PDF]

, 1995
We discuss the Sinai method of proving ergodicity of a discontinuous Hamiltonian system with (non-uniform) hyperbolic behavior.
Liverani, Carlangelo, Wojtkowski, Maciej P.   +1 more
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DISCRETE PORT HAMILTONIAN SYSTEMS [PDF]

IFAC Proceedings Volumes, 2005
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Talasila, V., Clemente Gallardo, J.J., van der Schaft, A.J.   +2 more
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Experimental study of tensor invariants of Hamiltonian systems [PDF]

Theoretical and Applied Mechanics
Typically, one considers the problem of finding the minimum number of invariants of a dynamical system sufficient for integrability. It can be also assumed that there are invariants not related to integrability that describe other properties of the ...
Tsiganov A. V.
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On the geometry of Hamiltonian vector fields [PDF]

E3S Web of Conferences, 2023
It is known that vector fields play an important role in many areas of mathematics and technology, in particular, in the theory of dynamical systems. Hamiltonian dynamical systems are generated by Hamiltonian vector fields. The paper studies the geometry
Narmanov Abdigappar, Diyarov Bekzod
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Multiple Solutions for Generalized Asymptotical Linear Hamiltonian Systems Satisfying Bolza Boundary Conditions

Journal of Applied Mathematics, 2013
This paper is devoted to multiple solutions of generalized asymptotical linear Hamiltonian systems satisfying Bolza boundary conditions. We classify the linear Hamiltonian systems by the index theory and obtain the existence and multiplicity of solutions
Yuan Shan, Baoqing Liu
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On the perturbations of a Hamiltonian system

Computers & Mathematics with Applications, 2011
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yingjing Hu, Lixia Duan, Yi Huang, Yuhai Wu   +3 more
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A new hierarchy of integrable system of 1+2 dimensions: from Newton's law to generalized Hamiltonian system. Part II

International Journal of Mathematics and Mathematical Sciences, 2006
The Hamiltonian equation provides us an alternate description of the basic physical laws of motion, which is used to be described by Newton's law.
Xuncheng Huang, Guizhang Tu
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Combining finite element space-discretizations with symplectic time-marching schemes for linear Hamiltonian systems

Frontiers in Applied Mathematics and Statistics, 2023
We provide a short introduction to the devising of a special type of methods for numerically approximating the solution of Hamiltonian partial differential equations.
Bernardo Cockburn, Shukai Du, Manuel A. Sánchez   +2 more
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Stabilization of Hamiltonian systems [PDF]

Nonlinear Analysis: Theory, Methods & Applications, 1986
Stabilization of Hamiltonian control systems is considered, using the first and the second Lypunov method. As the main result sufficient conditions are stated for an analytic Hamiltonian control system to be made locally asymptotically stable by an extended output feedback i.e. both the outputs and their derivatives are fed back.
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