
	Where results make sense

Topic: Hamiltonian equations

Related Topics

Hamiltonian path

Hamiltonian cycle

Hamiltonian group

Hamiltonian cycle problem

Hamiltonian path problem

Hamiltonian system

nonrelativistic Hamiltonian

Hamiltonian operator

Hamiltonian flow

Hamiltonian equations

Hamiltonian of a charged particle

In the News (Wed 3 Dec 08)

Goldman Sachs

Delta Air Lines

Saxby Chambliss

Damian Green

Sumner Redstone

Crimson Tide

Tommy Tuberville

Bill Clinton

Wayne Rooney

Vilasrao Deshmukh

	Hamiltonian mechanics - Wikipedia, the free encyclopedia
		Hamiltonian mechanics is a re-formulation of classical mechanics that was invented in 1833 by William Rowan Hamilton.
		The Hamiltonian induces a special vector field on the symplectic manifold, known as the symplectic vector field.
		The solutions to the Hamilton-Jacobi equations for this Hamiltonian are then the same as the geodesics on the manifold.
	en.wikipedia.org /wiki/Hamiltonian_mechanics (1321 words)

	Flow Equations for Hamiltonians
		The aim is to generate a bound state equation in a quantum field theory, particularly to derive an effective Hamiltonian which is practically solvable in Fock-spaces with reduced particle number, such that the approach can ultimately be used to address to the same problem for quantum chromodynamics.
		The flow equations describing the continuous unitary transformation which brings the Hamiltonian closer to diagonality are derived and solved exactly for the Lipkin model in the Holstein-Primakoff boson representation and for a large particle number N.
		The finite-size Tomonaga-Luttinger Hamiltonian with an arbitrary delta impurity at weak electron-electron interaction is mapped onto a non-interacting Fermi gas with renormalized impurity potential by means of flow equations for Hamiltonians.
	www.tphys.uni-heidelberg.de /~statphys/flowownabs.html (4033 words)

	Hamiltonian
		These Euler-Lagrange equations assert that the partial time derivative of the partial derivative of the Lagrangian relative to the speed component minus the partial derivative of the Lagrangian relative to the corresponding position component (for a given direction in space) exactly vanishes.
		The Hamiltonian equations assert, firstly, that the speed component is the partial derivative of the Hamiltonian with respect to the corresponding momentum component.
		We start in the Hamiltonian picture and define finite "canonical transformations" as new positions (Q) and their canonical momenta (P) that are each functions of both old positions (q) and their canonical momenta (p) in such a way that the Hamiltonian equations retain the same form under the transformation.
	www.qedcorp.com /pcr/pcr/hamilton.html (1214 words)

	[No title] (Site not responding. Last check: 2007-10-29)
		Hamiltonian equations of motion for a nonrelativistic charged particle in magnetospheric hydromagnetic perturbations are derived.
		The equations are gyroaveraged, allowing much larger time steps in numerical solutions of the equations of motion compared to integrating the full Lorentz equations of motion, but they contain finite-gyroradius effects to all orders in, where is the perpendicular wave number and is the particle gyroradius.
		The Hamiltonian conservation properties are useful for checking the accuracy of numerical integration schemes and they are essential for the use of Poincaré surface-of-section plots.
	www.agu.org /pubs/abs/nja/98JA01742/tmp.html (284 words)

	test answeres
		Hamiltonian equations live on cotangent bundle while Lagrange equations on a tangent bundle.
		However, Hamilton's equations require a choice of an "observer" (trivialization of the fiber bundle of histories).
		The Hamilton-Jacobi equations are most often introduced (obscurely) as a result of "canonical transformation of coordinates." But in fact -- HJ equations concern existence of a Lagrangian submanifold in the phase space on which a "wave-phase" is determined.
	www.math.siu.edu /kocik/cm/cm-ans.htm (480 words)

	Brian's RESEARCH STATEMENT (Site not responding. Last check: 2007-10-29)
		However, we have shown in the specific case of the sine-Gordon equation that initializing the scheme with a traveling wave solution of the modified equation yields a numerical solution of higher order accuracy, providing confirmation that the modified equations do, in fact, represent the numerical method.
		For the spatially discrete Nagumo equation with homogeneous diffusion there are analytic results concerning propagation failure of traveling waves for the problem with a piecewise linear approximation to the nonlinearity [2], and there are numerical results that suggest propagation failure for the nonlinear problem [7], depending on known parameters.
		Showing that the modified equations are an exact representation of the discretization and proving there are heteroclinic connections for this modified system would provide sufficient explanation of propagation failure for the original problem with small parameter values.
	www.math.uiowa.edu /~bemoore/research06.html (1375 words)

	Quantum Mathematics
		We develop a new technique to bring such singular equations to normal order (which differs from the usual normal order because it involves not the usual but the causal commutator); once this is done, most quantities of physical interest can be calculated simply by solving a linear equation.
		In the past ten years this type of equation has been widely used to build a multiplicity of phenomenological models in quantum optics, solidstate physics, quantum field theory, quantum measurement theory, etc. Thus the stochastic limit allows these phenomenological models to be deduced from the basic laws of physics.
		All the known types of master equations (and several new ones) are obtained just by taking the partial expectation of Langevin equations with respect to the reference state of the master field.
	www.wordtrade.com /science/mathematics/quantummath.htm (2115 words)

	Transactions of the American Mathematical Society
		Abstract: We derive estimates on the magnitude of non-adiabatic interaction between a Hamiltonian partial differential equation and a high-frequency nonlinear oscillator.
		Refining upon a similar result by Neishtadt for analytic ordinary differential equations, the temporal estimate crucially depends on the spatial regularity of the initial condition.
		J. Pöschel, On Nekhoroshev estimates for a nonlinear Schrödinger equation and a theorem by Bambusi.
	www.ams.org /tran/2003-355-02/S0002-9947-02-03143-4/home.html (595 words)

	UPC-MAT-DGDSA Seminars
		Abstract: The talk is devoted to the description of the De Donder-Weyl (DW) theory in the calculus of variations as a manifestly covariant generalization of the hamiltonian formalism from mechanics to field theory.
		Furthermore, the existence of first integrals of these equations is analyzed, and the relation between Cartan-Noether symmetries and generalized symmetries of the system is discussed.
		The equations of motion for the case of nonholonomic constraints are obtained in both the vakonomic and nonholonomic formalisms from a variational principle.
	www-mat.upc.es /dgdsa/seminaris/semin99.html (1403 words)

	Untitled Document
		Solution of Newton's equations of motion for forces that are: conservative, velocity-dependent, time-dependent, impulsive, position-dependent, systems with variable mass.
		Equations of constraint, generalized coordinates, Euler's equations with constraints.
		Reduced mass, two-body central force, equations of motion, differential equation of orbit, inverse square law, Kepler's laws, stability of circular orbits, closure.
	www.pas.rochester.edu /~cline/P235/Syllabus.htm (244 words)

	4 Hamiltonian mechanics (Site not responding. Last check: 2007-10-29)
		In Hamiltonian mechanics we use generalized momentum in place of velocity as a coordinate.
		The Lagrangian equation of motion 5 becomes a pair of equations known as the Hamiltonian system of equations:
		This is exactly the second equation of the system 23.
	alamos.math.arizona.edu /~rychlik/557-dir/mechanics/node4.html (201 words)

	Zitterbewegung
		Relativity and spinorial properties are not the only obstreperous features of the Dirac equation, as one discovers when he begins to obtain explicit solutions and to delve further into the properties of that equation.
		Here it is to be seen that the position operator consists, as we would expect, of the sum of an initial position vector, a displacement which is proportional to the elapsed time, and finally an unexpected term which represents a violent oscillation of the particle with an amplitude equal to its Compton wavelength.
		Thus, by 1950 there had emerged a fairly clear idea of the significance of the four components of the Dirac wave equation, that they corresponded to the occurrence of two energy states and two spin states, and some of the complications which their existence could produce.
	delta.cs.cinvestav.mx /~mcintosh/comun/symm/node11.html (1683 words)

	dynamical and control systems '03
		We study the boundary controllability of a nonlinear Korteweg-de Vries equation with the Dirichlet boundary condition on an interval with a critical length for which it has been shown by Rosier that the linearized control system around the origin is not controllable.
		Second, to a Hamiltonian formed by a pendulum and a rotor, to show the existence of trajectories with arbitrary increasing of energy when a general periodic non-autonomous Hamiltonian perturbation is added to the system.
		The simulation of singular nonlinear transport equation is obtained viacorresponding neutron or photon kinetic equation.
	www.sissa.it /fa/workshop_old/DCS2003/Program.html (4178 words)

	Matches for:
		In recent years, researchers have found new topological invariants of integrable Hamiltonian systems of differential equations and have constructed a theory for their topological classification.
		In particular, this collection covers the new topological invariants of integrable equations, the new topological obstructions to integrability, a new Morse-type theory of Bott integrals, and classification of bifurcations of the Liouville tori in integrable systems.
		Fomenko -- Theory of rough classification of integrable nondegenerate Hamiltonian differential equations on four-dimensional manifolds.
	www.mathaware.org /bookstore?fn=20&arg1=advsovseries&item=ADVSOV-6 (314 words)

	[No title]
		The goal of this tutorial is to present the Lagrangian and Hamiltonian formalism of mechanics.
		This equation implies that if the ends of the perturbation path are clamped at the ends, i.e.
		In papers which were published in the third volume, Lagrange studied the integration of differential equations and made various applications to topics such as fluid mechanics (where he introduced the Lagrangian function).
	www.resonancepub.com /lagrangian.htm (4349 words)

	UPC-MAT-DGDSA Seminars (Site not responding. Last check: 2007-10-29)
		Abstract: It is well known that field equations, derived from a variational principle, possess two different notions of energy-momentum tensors: the first one based on symmetries of the underlying variational functional (the Noether-like energy-momentum tensor), and the second one obtained from a variational extension of the field equations (variational energy-momentum tensors).
		Since, in this setting, Hamilton equations become equations for integral sections of a differential system, it is possible to understand the concepts of regularity and of Legendre transformation geometrically as properties of the Hamiltonian differential system.
		This geometric object is suitable for the study of singular differential equations which are affine in the velocities.
	www-mat.upc.es /dgdsa/seminars.html (984 words)

	The Maxwell-Vlasov Equations in Euler-Poincaré Form (Site not responding. Last check: 2007-10-29)
		Low's well known action principle for the Maxwell-Vlasov equations of ideal plasma dynamics was originally expressed in terms of a mixture of Eulerian and Lagrangian variables.
		Because of degeneracies in the Lagrangian, the Legendre transform is dealt with using the Dirac theory of constraints.
		Another Maxwell-Vlasov Poisson structure is known, whose ingredients are the Lie-Poisson bracket on the dual of the Lie algebra of symplectomorphisms of phase space and the Born-Infeld brackets for the Maxwell field.
	www.cds.caltech.edu /~marsden/bib/1998/01-CeHoHoMa1998 (231 words)

	5 Motion of a body in a rotating coordinate system (Site not responding. Last check: 2007-10-29)
		5.2.1 Newton's equations of motion in new coordinates
		The interpretation of these equations is that the fact that in a rotating coordinate system there are additional forces acting upon the body, represented by the three additional terms in the right-hand side of this equation.
		The extra two terms translate into the additional terms in the equations of motion which were called Coriolis, centripetal and inertia forces.
	alamos.math.arizona.edu /~rychlik/557-dir/mechanics/node5.html (478 words)

	Computational Mathematics And Mathematical Physics. (Site not responding. Last check: 2007-10-29)
		A.A. Abramov, A.A. Aslanyan, K. Balla, A comparison of the solutions of the sweep equations for Hamiltonian linear systems, in the case where the boundary conditions are transferred from infinity, Computational Mathematics And Mathematical Physics 35 (12) (1995) pp.
		A.A. Amosov, A.A. Zlotnik, An estimate of the error of quasi-averaging of the equations of motion of a viscous barotropic medium with rapidly oscillating data, Computational Mathematics And Mathematical Physics 36 (10) (1996) pp.
		A.A. Amosov, A.A. Zlotnik, Quasi-averaged equations of the one-dimensional motion of a viscous barotropic medium with rapidly oscillating data, Computational Mathematics And Mathematical Physics 36 (2) (1996) pp.
	www1.elsevier.com /cdweb/journals/09655425/viewer.htt?viewtype=authors (901 words)

	Hamilton’s equations
		The Hamiltonian of a system is expresses in terms of the generalized coordinates and the generalized momenta of the system,
		, or contact transformations are a special class of transformations which preserve the structure of the canonical equations, i.e.
		H is the Hamiltonian and f is an arbitrary function.
	electron6.phys.utk.edu /phys594/Tools/mechanics/summary/canonical/canonical.htm (131 words)

	Research Interests Gianne Derks
		They are dynamical systems of ordinary differential equations or partial differential equations with some extra structure.
		In physical models an example of a Hamiltonian system is a system which conserves the energy, like an undamped pendulum or a non-viscous fluid.
		Relation between blow-up in nonlinear Schrodinger equations and the behaviour of solutions in the generalised complex Ginzburg-Landau equations.
	www.mcs.surrey.ac.uk /Personal/G.Derks/research.html (508 words)

	The Hamiltonian formulation of classical mechanics
		The Hamiltonian of a system is defined to be the sum of the kinetic and potential energies expressed as a function of positions and their conjugate momenta.
		The solution of Hamilton's equations of motion will yield a trajectory in terms of positions and momenta as functions of time.
		Again, Hamilton's equations can be easily shown to be equivalent to Newton's equations, and, like the Lagrangian formulation, Hamilton's equations can be used to determine the equations of motion of a system in any set of coordinates.
	www.nyu.edu /classes/tuckerman/stat.mech/lectures/lecture_1/node4.html (329 words)

	Magnetic Pendulum: Mathematical Solution
		These are time-dependent variables which can be calculated using Hamilton's equations, a general method for computing position and momentum as a function of time.
		The kinetic energy is a function of pseudo-forces that arise from polar coordinate notation, i.e., centrifugal force and coriolis forces.
		To obtain the remaining Hamiltonian equations, it is necessary to sum the forces and take their derivative.
	www.apollowebworks.com /russell/am157s/math.html (647 words)

	Increment formulations for rounding error reduction in the numerical solution of structured differential systems -- ...
		Strategies for reducing the effect of cumulative rounding errors in geometric numerical integration are outlined.
		The focus is, in particular, on the solution of separable Hamiltonian systems using explicit symplectic integration methods and on solving orthogonal matrix differential systems using projection.
		Examples are given that demonstrate the advantages of an increment formulation over the standard implementation of conventional integrators.
	library.wolfram.com /infocenter/Articles/5406 (141 words)

	Ayhan Aydin (Site not responding. Last check: 2007-10-29)
		We consider completely integrable Hamiltonian equations like Euler-Poisson equations of a rigid body around a fixed point and Kirchoff equations describing the motion of a particle in an ideal fluid.
		Numerical solutions reveals that the Hamiltonian, Casimirs and the additional integral errors remain bounded for long-time integration for both methods.
		The periodicity of the numerical solutions are retained the Hamiltonian splitting method.
	www.math.metu.edu.tr /academic/aydin_ayhan.html (119 words)

	Eduard-Wilhelm Kirr's Research
		Existence and stability of coherent structures (bound states, solitons, kinks) in Hamiltonian equations.
		Parametric resonance of ground states in the nonlinear Schroedinger equation
		Existence and continuous dependence on data of the positive solutions of an integral equation from biomathematics
	www.math.uiuc.edu /~ekirr/page/research.html (381 words)

	Publications
		Alber, M.S. and S.J. Alber [1987], Hamiltonian formalism for nonlinear Schrodinger equations and sine-Gordon equations, J. London Math.
		In Integrability: the Seiberg-Witten and Whitham equations", eds H.W. Braden and I.M. Krichever, 1-10.
		Alber, M.S. and Yu.N. Fedorov [2000], Wave Solutions of Evolution Equations and Hamiltonian Flows on Nonlinear Subvarieties of Generalized Jacobians, J.Phys.A: Math.Gen. 33 8409-8425.
	www.nd.edu /~malber/publications.htm (1245 words)

	Luigi Chierchia Home Page (english)
		Prix 1995 Institut Henri Poincaré for the paper "Drift and diffusion in phase space", Ann.
		Director of the local unit Roma TRE for the project MURST/ MIUR 1998-2000-2002-2004 ("Variational methods and nonlinear differential equations", national director A. Ambrosetti).
		Hamiltonian stability of spin-orbit resonances in Celestial Mechanics
	www.mat.uniroma3.it /users/chierchia/WWW/english_version.html (803 words)

	Oscar Gonzalez: Numerical Methods
		For Hamiltonian systems with symmetry it is thus generally desirable that numerical time integration schemes preserve physically meaningful integrals from the underlying system.
		Modified equations are a concept from backward error analysis that characterize discretization errors in a numerical method.
		Thus, results from Hamiltonian perturbation theory can be used to gain insight into the behavior of symplectic methods.
	www.ma.utexas.edu /users/og/numerics.html (1123 words)

Try your search on: Qwika (all wikis)