Theory and praxis of map analsys in CHEF part 2: Nonlinear normal form

Michelotti, Leo ; /FERMILAB

关键词: 99 GENERAL AND MISCELLANEOUS//MATHEMATICS;    COMPUTING;    AND INFORMATION SCIENCE;    ALGORITHMS;    HAMILTONIANS;    MAINTENANCE;    NAVIGATION;    PERTURBATION THEORY;    PHYSICS;    TRANSFORMATIONS;    WATERSHEDS Accelerators;    Computing;   

DOI  :  10.2172/966182
RP-ID  :  FERMILAB-FN-0837-APC-CD
PID  :  OSTI ID: 966182
Others  :  TRN: US0903961

学科分类：核物理和高能物理

美国|英语

来源: SciTech Connect

【 摘 要 】

This is the second of three memos describing how normal form map analysis is implemented in CHEF. The first [1] explained the manipulations required to assure that initial, linear transformations preserved Poincare invariants, thereby confirming correct normalization of action-angle coordinates. In this one, the transformation will be extended to nonlinear terms. The third, describing how the algorithms were implemented within the software of CHEF's libraries, most likely will never be written. The first section, Section 2, quickly lays out preliminary concepts and relationships. In Section 3, we shall review the perturbation theory - an iterative sequence of transformations that converts a nonlinear mapping into its normal form - and examine the equation which moves calculations from one step to the next. Following that is a section titled 'Interpretation', which identifies connections between the normalized mappings and idealized, integrable, fictitious Hamiltonian models. A final section contains closing comments, some of which may - but probably will not - preview work to be done later. My reasons for writing this memo and its predecessor have already been expressed. [1] To them can be added this: 'black box code' encourages users to proceed with little or no understanding of what it does or how it operates. So far, CHEF has avoided this trap admirably by failing to attract potential users. However, we reached a watershed last year: even I now have difficulty following the software through its maze of operations. Extensions to CHEF's physics functionalities, software upgrades, and even simple maintenance are becoming more difficult than they should. I hope these memos will mark parts of the maze for easier navigation in the future. Despite appearances to the contrary, I tried to include no (or very little) more than the minimum needed to understand what CHEF's nonlinear analysis modules do.1 As with the first memo, material has been lifted - and modified - from Intermediate Classical Dynamics (ICD) [2], old technical memos, seminar viewgraphs, and lecture notes. Finally, for a reason I do not know but am willing to indulge, equation and comment labels start from where they left off in Part 1.