Dynamics of classical quadrupole moment. II
type: Item
instance of: scholarly article
title: Dynamics of classical quadrupole moment. II
zbMATH Open document ID: 1019.81062
DOI: 10.1016/S0960-0779(01)00071-6
author: Shigetoku Kawabata
author: Masahiko Tokita
published in: Chaos, Solitons and Fractals
publication date: 2002-08-18T00:00:00Z
review text: This is the second part of an interesting paper, for Part I see the same authors [ibid. 13, 997-1015 (2002; Zbl 1018.81055)]. In Part I they studied the motion of the electric quadrupole moment of the nucleus perturbed by the alternating magnetic field whose dynamics leads directly to an iterative map. The classical equations of motion of the quadrupole moment were introduced there. In the present paper the authors study behaviour of orbits of the reversible area-preserving map, as the perturbation parameter is varied. Some numerical methods are used for this purpose. The advantage is to make use of the symmetry of the map to reduce the problem of finding a periodic orbit to one of finding the root of a function of one variable. It is known that the map is a product of two involutions. An example of symmetry in chaos is presented. The mechanism of transition of chaos, which is of fundamental importance for understanding the phenomenon of chaotic behaviour, is discussed. A homoclinic orbit is shown. The type of motion of the system can be altered as the value of the parameter is changed. The bifurcation diagram is discussed. The determination of bifurcation value of system parameter for various types of periodic responses is one of the central problems. Newton's method is effectively used for finding the bifurcation value. The Jacobian matrix is evaluated by the solutions of variational equations. A set of bifurcation values in the parameter space is obtained. A technique for distinguishing between chaotic and nonchaotic motion is given.
Mathematics Subject Classification ID: 81V35
Mathematics Subject Classification ID: 81Q50
Mathematics Subject Classification ID: 37N20
Mathematics Subject Classification ID: 34C23
zbMATH DE Number: 1783150
zbMATH Keywords: electric quadrupole moment
zbMATH Keywords: magnetic moment operator
zbMATH Keywords: chaotic system
zbMATH Keywords: Poincaré map
zbMATH Keywords: Hamiltonian
zbMATH Keywords: spin operator
zbMATH Keywords: kicked rotor
reviewed by: Dimitar A. Kolev
MaRDI profile type: Publication
cites work: Dynamics of classical quadrupole moment. I
cites work: Bifurcation of periodic responses in forced dynamic nonlinear circuits: Computation of bifurcation values of the system parameters
cites work: Universal behaviour in families of area-preserving maps
cites work: Determining Lyapunov exponents from a time series
full work available at URL: s0960-0779(01)00071-6
OpenAlex ID: W1967324756
description: scientific article; zbMATH DE number 1783150