Hamiltonian form of general averaged systems

1992 ◽  
Vol 3 (1) ◽  
pp. 115-123
Author(s):  
Yu. G. Pavlenko ◽  
S. I. Zelenskii
Keyword(s):  
Hamiltonian Form ◽  
Averaged Systems

Kinetic theory

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Distribution Function ◽  
Kinetic Theory ◽  
Liouville Equation ◽  
Vlasov Equation ◽  
Particle Distribution ◽  
Equations Of Motion ◽  
Poisson Brackets ◽  
Hamiltonian Form ◽  
First Order ◽  
Number Of Particles

This chapter covers the equations governing the evolution of particle distribution and relates the macroscopic thermodynamical quantities to the distribution function. The motion of N particles is governed by 6N equations of motion of first order in time, written in either Hamiltonian form or in terms of Poisson brackets. Thus, as this chapter shows, as the number of particles grows it becomes necessary to resort to a statistical description. The chapter first introduces the Liouville equation, which states the conservation of the probability density, before turning to the Boltzmann–Vlasov equation. Finally, it discusses the Jeans equations, which are the equations obtained by taking various averages over velocities.

scholarly journals Qualitative stability and synchronicity analysis of power network models in port-Hamiltonian form

2018 ◽  
Vol 28 (10) ◽  
pp. 101102 ◽  
Author(s):  
Volker Mehrmann ◽  
Riccardo Morandin ◽  
Simona Olmi ◽  
Eckehard Schöll
Keyword(s):  
Network Models ◽  
Hamiltonian Form ◽  
Power Network

scholarly journals A new hierarchy of integrable system of1+2dimensions: from Newton's law to generalized Hamiltonian system. Part II

2006 ◽  
Vol 2006 ◽  
pp. 1-10
Author(s):  
Xuncheng Huang ◽  
Guizhang Tu
Keyword(s):  
Integrable System ◽  
Integrable Systems ◽  
Hamiltonian Equation ◽  
Hamiltonian Form ◽  
Fundamental Interest ◽  
Newton's Law ◽  
Newton’S Law ◽  
System Part ◽  
Generalized Hamiltonian System ◽  
Physical Laws

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. The research on Hamiltonian integrable systems is one of the most important topics in the theory of solitons. This article proposes a new hierarchy of integrable systems of1+2dimensions with its Hamiltonian form by following the residue approach of Fokas and Tu. The new hierarchy of integrable system is of fundamental interest in studying the Hamiltonian systems.

Boson Hamiltonians and stochasticity for the vorticity equation

1990 ◽  
Vol 68 (9) ◽  
pp. 719-722 ◽  
Author(s):  
Hubert H. Shen
Keyword(s):  
Viscous Flow ◽  
Inviscid Flow ◽  
Vorticity Equation ◽  
Hamiltonian Form ◽  
Bose Operators

The evolution of the vorticity in time for 2D inviscid flow and in Lagrangian time for 3D viscous flow is written in Hamiltonian form by introducing Bose operators. The addition of the viscous and convective terms, respectively, leads to an interpretation of the Hamiltonian contribution to the evolution as Langevin noise.

On Integrals developable about a Singular Point of a Hamiltonian System of Differential Equations

1924 ◽  
Vol 22 (3) ◽  
pp. 325-349 ◽  
Author(s):  
T. M. Cherry
Keyword(s):  
Singular Point ◽  
Hamiltonian System ◽  
Characteristic Function ◽  
Differential Equations ◽  
Convergent Series ◽  
Hamiltonian Form ◽  
System Of Differential Equations ◽  
Image Position

Letbe a system of differential equations of Hamiltonian form, the characteristic function H being independent of t and expansible in a convergent series of powers of x1, … xn, y1, … yn in which the terms of lowest degree are

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