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Hamiltonian Systems (hamiltonian + system)

Distribution by Scientific Domains

Engineering	69%
Mathematics and Statistics	23%

Selected Abstracts

Suppressing local particle oscillations in the Hamiltonian particle method for elasticity

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 12 2010
Masahiro Kondo
Abstract The governing equation of elasticity is discretized into motion equations of the particles in a Hamiltonian system. A weighted least-square method is adopted to evaluate the Green,Lagrange strain. Using a symplectic scheme for the Hamiltonian system, we obtain the property of energy conservation in the discretized calculations. However, local particle oscillations occur, and they excessively decrease low frequency motion. In this study, we propose the use of an artificial potential force to suppress the local oscillations. The accuracy of the model with and without the inclusion of the artificial force is examined by analyzing a cantilever beam and wave propagation. With the inclusion of the artificial force, the local oscillations are reduced while energy conservation is maintained. Copyright © 2009 John Wiley & Sons, Ltd. [source]

An objective finite element approximation of the kinematics of geometrically exact rods and its use in the formulation of an energy,momentum conserving scheme in dynamics

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 12 2002
I. Romero
Abstract We present in this paper a new finite element formulation of geometrically exact rod models in the three-dimensional dynamic elastic range. The proposed formulation leads to an objective (or frame-indifferent under superposed rigid body motions) approximation of the strain measures of the rod involving finite rotations of the director frame, in contrast with some existing formulations. This goal is accomplished through a direct finite element interpolation of the director fields defining the motion of the rod's cross-section. Furthermore, the proposed framework allows the development of time-stepping algorithms that preserve the conservation laws of the underlying continuum Hamiltonian system. The conservation laws of linear and angular momenta are inherited by construction, leading to an improved approximation of the rod's dynamics. Several numerical simulations are presented illustrating these properties. Copyright © 2002 John Wiley & Sons, Ltd. [source]

Stabilization of an underactuated bottom-heavy airship via interconnection and damping assignment

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 18 2007
Zili Cai
Abstract This paper focuses on feedback stabilization of a neutrally buoyant and bottom-heavy airship actuated by only five independent controls (with the rolling motion underactuated). The airship is modelled as an eudipleural submerged rigid body whose dynamics is formulated as a Hamiltonian system with respect to a Lie,Poisson structure. By exploiting the geometrical structure and using the so-called interconnection and damping assignment (IDA) passivity-based methodology for port-controlled Hamiltonian systems, state feedback control laws asymptotically stabilizing two typical motions are designed via La Salle invariance principle and Chetaev instability theorem. Simulation results verify the control laws. Copyright © 2007 John Wiley & Sons, Ltd. [source]

Dynamical modeling of chaos single-screw extruder and its three-dimensional numerical analysis

POLYMER ENGINEERING & SCIENCE, Issue 3 2000
W. R. Hwang
The Chaos Screw (CS) nonlinear dynamical model is proposed to describe the development of chaos in a single-screw extrusion process and the model is verified by three-dimensional numerical simulations. The only-barrier channel is the unperturbed Hamiltonian system, which consists of two homoclinic orbits and nested elliptic tori of nonlinear oscillation in periodic (extended) state space. A periodically inserted no-barrier zone represents a perturbation. For small perturbations, homoclinic tangle leads to the Cantor set near the homoclinic fixed point and elliptic rotations are changed into the resonance bands or KAM tori, depending on the commensurability of frequency ratio of the corresponding orbits. A finite element method of multivariant Q,1+PO elements is applied to solve the velocity fields and a 4th order Runge-Kutta method is used for the particle tracing. The resulting Poincaré section verifies the proposed dynamical model, showing the resonance band corresponding to rotation number 1/3 under small perturbations. As the strength of perturbation increases, the Poincaré sections indicate wider stochastic regions in which random particle motions take place. [source]

A note on energy conservation for Hamiltonian systems using continuous time finite elements

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 12 2001
Peter HansboArticle first published online: 5 NOV 200
Abstract In this note we suggest a new approach to ensure energy conservation in time-continuous finite element methods for non-linear Hamiltonian problems. Copyright © 2001 John Wiley & Sons, Ltd. [source]

Lie-Poisson integrators: A Hamiltonian, variational approach

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 13 2010
Zhanhua Ma
Abstract In this paper we present a systematic and general method for developing variational integrators for Lie-Poisson Hamiltonian systems living in a finite-dimensional space ,,*, the dual of Lie algebra associated with a Lie group G. These integrators are essentially different discretized versions of the Lie-Poisson variational principle, or a modified Lie-Poisson variational principle proposed in this paper. We present three different integrators, including symplectic, variational Lie-Poisson integrators on G×,,* and on ,,×,,*, as well as an integrator on ,,* that is symplectic under certain conditions on the Hamiltonian. Examples of applications include simulations of free rigid body rotation and the dynamics of N point vortices on a sphere. Simulation results verify that some of these variational Lie-Poisson integrators are good candidates for geometric simulation of those two Lie-Poisson Hamiltonian systems. Copyright © 2009 John Wiley & Sons, Ltd. [source]

Conservation properties of a time FE method.

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 13 2005
Part IV: Higher order energy, momentum conserving schemes
Abstract In the present paper a systematic development of higher order accurate time stepping schemes which exactly conserve total energy as well as momentum maps of underlying finite-dimensional Hamiltonian systems with symmetry is shown. The result of this development is the enhanced Galerkin (eG) finite element method in time. The conservation of the eG method is generally related to its collocation property. Total energy conservation, in particular, is obtained by a new projection technique. The eG method is, moreover, based on objective time discretization of the used strain measure. This paper is concerned with particle dynamics and semi-discrete non-linear elastodynamics. The related numerical examples show good performance in presence of stiffness as well as for calculating large-strain motions. Copyright © 2005 John Wiley & Sons, Ltd. [source]

Analysis and synthesis of perturbed Duffing oscillators

INTERNATIONAL JOURNAL OF CIRCUIT THEORY AND APPLICATIONS, Issue 3 2006
V. N. Savov
Abstract Analysis and synthesis of perturbed Duffing oscillators have been presented. The oscillations in such systems are regarded as limit cycles in perturbed Hamiltonian systems under polynomial perturbations of sixth degree and are analysed by using the Melnikov function. It has been proved that there exists a polynomial perturbation depending on the zeros of the Melnikov function so that the system considered can have either two simple limit cycles, or one limit cycle of multiplicity 2, or one simple limit cycle. A synthesis of such oscillators based on the Melnikov's theory has been proposed. Copyright © 2006 John Wiley & Sons, Ltd. [source]

Stabilization of an underactuated bottom-heavy airship via interconnection and damping assignment

Two singular point linear Hamiltonian systems with an interface condition

MATHEMATISCHE NACHRICHTEN, Issue 3 2010
Horst Behncke
Abstract We consider the problem of a linear Hamiltionian system on , with an interface condition which we take to be at x = 0. Assuming limit point conditions at ±,, we prove the problem is uniquely solvable, and a resolvent is constructed. Our method of solution is to map the problem onto a half line problem of double size and apply the theory of half line problems. A Titchmarsh-Weyl function is associated with the problem, and a unitary transform is constructed which maps the differential operator onto the multiplication operator in the Hilbert space determined by the spectral function , (© 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

Adaptive L2 Disturbance Attenuation Of Hamiltonian Systems With Parametric Perturbation And Application To Power Systems

ASIAN JOURNAL OF CONTROL, Issue 1 2003
Tielong Shen
ABSTRACT This paper deals with the problem of L2 disturbance attenuation for Hamiltonian systems. We first show that the L2 gain from the disturbance to a penalty signal may be reduced to any given level if the penalty signal is defined properly. Then, an adaptive version of the controller will be presented to compensate the parameter perturbation. When the perturbed parameters satisfy a suitable matching condition, it is easy to introduce the adaptive mechanism to the controller. Another contribution of this paper is to apply the proposed method to the excitation control problem for power systems. An adaptive L2 controller for the power system is designed using the proposed method and a simulation result with the proposed controller is given. [source]

Symplectic rigidity, symplectic fixed points, and global perturbations of Hamiltonian systems

COMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 3 2008
Dragomir L. Dragnev
In this paper we study a generalized symplectic fixed-point problem, first considered by J. Moser in [20], from the point of view of some relatively recently discovered symplectic rigidity phenomena. This problem has interesting applications concerning global perturbations of Hamiltonian systems. © 2007 Wiley Periodicals, Inc. [source]

Purely nonlinear instability of standing waves with minimal energy

COMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 11 2003
Andrew Comech
We consider Hamiltonian systems with U(1) symmetry. We prove that in the generic situation the standing wave that has the minimal energy among all other standing waves is unstable, in spite of the absence of linear instability. Essentially, the instability is caused by higher algebraic degeneracy of the zero eigenvalue in the spectrum of the linearized system. We apply our theory to the nonlinear Schrödinger equation. © 2003 Wiley Periodicals, Inc. [source]