Extracting dynamical frequencies from invariants of motion in finite-dimensional nonlinear integrable systems.
Phys Rev E
; 103(6-1): 062216, 2021 Jun.
Article
en En
| MEDLINE
| ID: mdl-34271647
ABSTRACT
Integrable dynamical systems play an important role in many areas of science, including accelerator and plasma physics. An integrable dynamical system with n degrees of freedom possesses n nontrivial integrals of motion, and can be solved, in principle, by covering the phase space with one or more charts in which the dynamics can be described using action-angle coordinates. To obtain the frequencies of motion, both the transformation to action-angle coordinates and its inverse must be known in explicit form. However, no general algorithm exists for constructing this transformation explicitly from a set of n known (and generally coupled) integrals of motion. In this paper we describe how one can determine the dynamical frequencies of the motion as functions of these n integrals in the absence of explicitly known action-angle variables, and we provide several examples.
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Colección:
01-internacional
Banco de datos:
MEDLINE
Idioma:
En
Revista:
Phys Rev E
Año:
2021
Tipo del documento:
Article
País de afiliación:
Estados Unidos