TY - JOUR

T1 - Asymptotic behaviour of infinite chains of coupled kinematic points

T2 - Second-order equations

AU - Feintuch, Avraham

PY - 2014/1/1

Y1 - 2014/1/1

N2 - The behaviour of infinite chains of coupled kinematic points is studied. The points are second order, that is, they have mass. The chains could have been designed in any number of ways, including linear-quadratic optimal control. Behaviour means what happens as time goes to infinity. It is not assumed that the initial state is in the Hilbert space l 2 because it has been seen in our previous work that in some situations this assumption has anomalous results. Instead, the initial state taken to be l ∞. The finite-dimensional version of the infinite second-order system we study arises in physics in the theory of phonons.

AB - The behaviour of infinite chains of coupled kinematic points is studied. The points are second order, that is, they have mass. The chains could have been designed in any number of ways, including linear-quadratic optimal control. Behaviour means what happens as time goes to infinity. It is not assumed that the initial state is in the Hilbert space l 2 because it has been seen in our previous work that in some situations this assumption has anomalous results. Instead, the initial state taken to be l ∞. The finite-dimensional version of the infinite second-order system we study arises in physics in the theory of phonons.

KW - Distributed control

KW - Infinite-dimensional systems

KW - Mobile masses

KW - Phonons

KW - Second-order linear equations

UR - http://www.scopus.com/inward/record.url?scp=84906311520&partnerID=8YFLogxK

U2 - 10.1007/s00498-014-0125-y

DO - 10.1007/s00498-014-0125-y

M3 - Article

AN - SCOPUS:84906311520

VL - 26

SP - 463

EP - 480

JO - Mathematics of Control, Signals, and Systems

JF - Mathematics of Control, Signals, and Systems

SN - 0932-4194

IS - 3

ER -