STABILITY AND AMPLITUDE RANGES OF TWO DIMENSIONAL NON-LINEAR OSCILLATIONS WITH PERIODICAL HAMILTONIAN applied to betatron oscillations in circular particle accelerators PartⅠ and PartⅡ

摘要

We consider a mechanical system of two degrees of freedom, which can be described by a system of canonical differential equations. The Hamiltonian is supposed to be explicitly time-dependent with period 2fr. The aim is to bring this system by a sequence of canonical and periodical transformations into a form, where the new Hamiltonian is constant and as simple as possible.nThe general theory, which was developed in Part I, will here be brought to a stage, where it becomes immediately applicable to given particular cases. Some formulae refer particularly to circular particle accelerators, some are applicable to any system, to which the general theory applies.