Nonlinear dynamics Available to Purchase

Following an introduction on analytical mechanics, canonical transformations, and perturbation theory, a description is given of nonlinear effects for near‐integrable systems associated with resonances, amplitude variations with multiple crossings, adiabatic changes of the parameters, and time variation of the perturbation. Examples of applications coming from observations and calculations related to CERN accelerators concern coupling measurements, intra‐beam scattering, beam‐beam effects magnetic imperfections, two‐beam overlap knockout, and synchro‐betatron resonances. Finally, the notions of invariant distortion and aperture of bounded motion in the presence of multipoles are introduced.