Journal
PHYSICAL REVIEW ACCELERATORS AND BEAMS
Volume 24, Issue 6, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevE.103.062216
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Funding
- Office of Science of the US Department of Energy [DE-AC02-05CH11231, DEAC0207CH11359]
- US DOE Early Career Research Program under the Office of High Energy Physics
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This paper describes how to determine the dynamical frequencies of motion as functions of integrals in the absence of explicitly known action-angle variables, and provides several examples.
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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