Theory and praxis pf map analsys in CHEF part 1: Linear normal form

Thumbnail image of item number 1 in: 'Theory and praxis pf map analsys in CHEF part 1: Linear normal form'.
Thumbnail image of item number 2 in: 'Theory and praxis pf map analsys in CHEF part 1: Linear normal form'.
Thumbnail image of item number 3 in: 'Theory and praxis pf map analsys in CHEF part 1: Linear normal form'.
Thumbnail image of item number 4 in: 'Theory and praxis pf map analsys in CHEF part 1: Linear normal form'.
Showing 1-4 of 18 pages in this report.

PDF Version Also Available for Download.

Description

This memo begins a series which, put together, could comprise the 'CHEF Documentation Project' if there were such a thing. The first--and perhaps only--three will telegraphically describe theory, algorithms, implementation and usage of the normal form map analysis procedures encoded in CHEF's collection of libraries. [1] This one will begin the sequence by explaining the linear manipulations that connect the Jacobian matrix of a symplectic mapping to its normal form. It is a 'Reader's Digest' version of material I wrote in Intermediate Classical Dynamics (ICD) [2] and randomly scattered across technical memos, seminar viewgraphs, and lecture notes for the past ... continued below

Physical Description

18 pages

Creation Information

Michelotti, Leo October 1, 2008.

Context

This report is part of the collection entitled: Office of Scientific & Technical Information Technical Reports and was provided by UNT Libraries Government Documents Department to Digital Library, a digital repository hosted by the UNT Libraries. More information about this report can be viewed below.

Who

People and organizations associated with either the creation of this report or its content.

Author

Sponsor

Publisher

Provided By

UNT Libraries Government Documents Department

Serving as both a federal and a state depository library, the UNT Libraries Government Documents Department maintains millions of items in a variety of formats. The department is a member of the FDLP Content Partnerships Program and an Affiliated Archive of the National Archives.

About | Browse this Partner

Contact Us

Corrections Questions

What

Descriptive information to help identify this report. Follow the links below to find similar items on the Digital Library.

Description

This memo begins a series which, put together, could comprise the 'CHEF Documentation Project' if there were such a thing. The first--and perhaps only--three will telegraphically describe theory, algorithms, implementation and usage of the normal form map analysis procedures encoded in CHEF's collection of libraries. [1] This one will begin the sequence by explaining the linear manipulations that connect the Jacobian matrix of a symplectic mapping to its normal form. It is a 'Reader's Digest' version of material I wrote in Intermediate Classical Dynamics (ICD) [2] and randomly scattered across technical memos, seminar viewgraphs, and lecture notes for the past quarter century. Much of its content is old, well known, and in some places borders on the trivial.1 Nevertheless, completeness requires their inclusion. The primary objective is the 'fundamental theorem' on normalization written on page 8. I plan to describe the nonlinear procedures in a subsequent memo and devote a third to laying out algorithms and lines of code, connecting them with equations written in the first two. Originally this was to be done in one short paper, but I jettisoned that approach after its first section exceeded a dozen pages. The organization of this document is as follows. A brief description of notation is followed by a section containing a general treatment of the linear problem. After the 'fundamental theorem' is proved, two further subsections discuss the generation of equilibrium distributions and issue of 'phase'. The final major section reviews parameterizations--that is, lattice functions--in two and four dimensions with a passing glance at the six-dimensional version. Appearances to the contrary, for the most part I have tried to restrict consideration to matters needed to understand the code in CHEF's libraries.

Physical Description

18 pages

Language

Item Type

Identifier

Unique identifying numbers for this report in the Digital Library or other systems.

  • Report No.: FERMILAB-FN-0826-CD
  • Grant Number: AC02-07CH11359
  • DOI: 10.2172/946178 | External Link
  • Office of Scientific & Technical Information Report Number: 946178
  • Archival Resource Key: ark:/67531/metadc895955

Collections

This report is part of the following collection of related materials.

Office of Scientific & Technical Information Technical Reports

Reports, articles and other documents harvested from the Office of Scientific and Technical Information.

Office of Scientific and Technical Information (OSTI) is the Department of Energy (DOE) office that collects, preserves, and disseminates DOE-sponsored research and development (R&D) results that are the outcomes of R&D projects or other funded activities at DOE labs and facilities nationwide and grantees at universities and other institutions.

About | Browse this Collection

What responsibilities do I have when using this report?

Digital Files

When

Dates and time periods associated with this report.

Creation Date

  • October 1, 2008

Added to The UNT Digital Library

  • Sept. 27, 2016, 1:39 a.m.

Description Last Updated

  • Sept. 26, 2017, 12:42 p.m.

Usage Statistics

When was this report last used?

Yesterday: 0
Past 30 days: 0
Total Uses: 5
More Statistics

Interact With This Report

Here are some suggestions for what to do next.

Start Reading

Thumbnail image of item number 1 in: 'Theory and praxis pf map analsys in CHEF part 1: Linear normal form'.
Thumbnail image of item number 2 in: 'Theory and praxis pf map analsys in CHEF part 1: Linear normal form'.
Thumbnail image of item number 3 in: 'Theory and praxis pf map analsys in CHEF part 1: Linear normal form'.
Thumbnail image of item number 4 in: 'Theory and praxis pf map analsys in CHEF part 1: Linear normal form'.

PDF Version Also Available for Download.

Citations, Rights, Re-Use

International Image Interoperability Framework

IIF Logo

We support the IIIF Presentation API

Michelotti, Leo. Theory and praxis pf map analsys in CHEF part 1: Linear normal form, report, October 1, 2008; Batavia, Illinois. (digital.library.unt.edu/ark:/67531/metadc895955/: accessed December 10, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.