The Crane Foucault pendulum: An exercise in action‐angle variable perturbation theory

1983 ◽  
Vol 51 (2) ◽  
pp. 110-114 ◽  
Author(s):  
K. T. Hecht
Keyword(s):  
Perturbation Theory ◽  
Angle Variable ◽  
Foucault Pendulum ◽  
Action Angle Variable

Stability of Subharmonic Oscillations in a Pipe Conveying Fluid under Harmonic Excitation

2013 ◽  
Vol 444-445 ◽  
pp. 796-800
Author(s):  
Yi Xiang Geng ◽  
Han Ze Liu
Keyword(s):  
Averaging Method ◽  
Melnikov Method ◽  
Equation Of Motion ◽  
Harmonic Excitation ◽  
Angle Variable ◽  
Galerkin Approach ◽  
Existence And Stability ◽  
The Stability ◽  
Action Angle Variable ◽  
Conveying Fluid

The existence and stability of subharmonic oscillations in a two end-fixed fluid conveying pipe whose base is subjected to a harmonic excitation are investigated. A Galerkin approach is utilized to reduce the equation of motion to a second order nonlinear differential equation. The conditions for the existence of subharmonic oscillations are given by using Melnikov method. The stability of subharmonic oscillations is discussed in detail by using action-angle variable and averaging method. It is shown that the velocity of fluid plays an important role in the stability of subharmonic oscillations.

Quantum action‐angle‐variable analysis of basic systems

1987 ◽  
Vol 55 (3) ◽  
pp. 261-264 ◽  
Author(s):  
Robert A. Leacock ◽  
Michael J. Padgett
Keyword(s):  
Angle Variable ◽  
Quantum Action ◽  
Action Angle Variable ◽  
Variable Analysis

Quantum action-angle variable of the Hamilton–Jacobi theory in two dimensions

2006 ◽  
Vol 73 (5) ◽  
pp. 443-446 ◽  
Author(s):  
Gang Chen ◽  
Pei-cai Xuan ◽  
Jian-Li Wang
Keyword(s):  
Two Dimensions ◽  
Angle Variable ◽  
Quantum Action ◽  
Action Angle Variable

A Perturbation Theory for the Population of Atomic Energy Levels in Non-Lte Plasmas

1988 ◽  
Vol 102 ◽  
pp. 343-347
Author(s):  
M. Klapisch
Keyword(s):  
Perturbation Theory ◽  
Small Parameter ◽  
Classification Scheme ◽  
Sum Rules ◽  
Energy Levels ◽  
Natural Classification ◽  
Quantum Numbers ◽  
Formal Expansion ◽  
Atomic Energy Levels ◽  
As Effects

AbstractA formal expansion of the CRM in powers of a small parameter is presented. The terms of the expansion are products of matrices. Inverses are interpreted as effects of cascades.It will be shown that this allows for the separation of the different contributions to the populations, thus providing a natural classification scheme for processes involving atoms in plasmas. Sum rules can be formulated, allowing the population of the levels, in some simple cases, to be related in a transparent way to the quantum numbers.

Energy, Information, and Superluminal Speed in Quantum Electrodynamics

2020 ◽  
pp. 27-33
Author(s):  
Boris A. Veklenko
Keyword(s):  
Electromagnetic Field ◽  
Perturbation Theory ◽  
Quantum Electrodynamics ◽  
Excited Atom ◽  
Standard Quantum ◽  
Energy Information

Without using the perturbation theory, the article demonstrates a possibility of superluminal information-carrying signals in standard quantum electrodynamics using the example of scattering of quantum electromagnetic field by an excited atom.

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