Hamiltonian and Linear-Space Structure for Damped Oscillators: I. General Theory
Mathematical Physics
2007-05-23 v2 Dynamical Systems
math.MP
Rings and Algebras
Classical Physics
Abstract
The phase space of damped linear oscillators is endowed with a bilinear map under which the evolution operator is symmetric. This analog of self-adjointness allows properties familiar from conservative systems to be recovered, e.g., eigenvectors are "orthogonal" under the bilinear map and obey sum rules, initial-value problems are readily solved and perturbation theory applies to the_complex_ eigenvalues. These concepts are conveniently represented in a biorthogonal basis.
Cite
@article{arxiv.math-ph/0206026,
title = {Hamiltonian and Linear-Space Structure for Damped Oscillators: I. General Theory},
author = {S. C. Chee and Alec Maassen van den Brink and K. Young},
journal= {arXiv preprint arXiv:math-ph/0206026},
year = {2007}
}
Comments
REVTeX4, 10pp., 1 PS figure. N.B.: `Alec' is my first name, `Maassen van den Brink' my family name. v2: extensive streamlining