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<- [[:chaosbook]] ====== Chapter: Get straight ====== (ChaosBook.org blog, chapter [[http://chaosbook.org/paper.shtml#conjug|Get straight]]) --- //[[predrag.cvitanovic@physics.gatech.edu|Predrag Cvitanovic]] 2009-03-08// (the latest posts within a section at the top, blog-style) Needed for the semi-classical helium chapter, and for desymmetrization chapters, where coordinate changes are one way to map an equivariant flow into an invariantflow. Currently does not fit into the flow of the ChaosBook. --- //[[predrag.cvitanovic@physics.gatech.edu|Predrag Cvitanovic]] 2009-03-10// Nonlinear coordinate transformations are very important but we do not use them much in ChaosBook. This chapter collects in one place all that we will need. It is meant to be omitted on first reading, sections of it read later, when need arises. Necessary stuff: * cycle stabilities are metric invariants of flows * turn a Keplerian ellipse into a harmonic oscillator * regularize the 2-body Coulomb collisions in classical helium * what else? Rewrite the header of the chapter and the [[:chaosbook:conjug#resume|summary]] so the motivations (as listed in this blog) and the main results are written up and clear. ===== Section: Changing coordinates ===== Collect clearly and concisely formulas needed later on, especially for linearized flows ===== Section: Rectification of flows ===== Harmonic oscillator change of coordinates needed later to motivate Rossler flow, and equivarinat -to-> invariant coordinate changes. Perhaps make into a subsection? --- //[[predrag.cvitanovic@physics.gatech.edu|Predrag Cvitanovic]] 2009-03-10// ===== Section: Collinear helium ===== regularize the 2-body Coulomb collisions in classical helium. ===== Section: Rectification of maps ===== If material in [[chaosbook:noise|Chapter Noise]] gets sufficiently developed, up to how to include weka noise perturbative corrections (as a warm-up for the <latex>\hbar</latex> corrections), this material will be needed. Otherwise, move into an appendix? --- //[[predrag.cvitanovic@physics.gatech.edu|Predrag Cvitanovic]] 2009-03-10// ===== Section: Rectification of a periodic orbit ===== Perhaps make into a subsection of the preceding section? --- //[[predrag.cvitanovic@physics.gatech.edu|Predrag Cvitanovic]] 2009-03-10// ===== Section: Missing material? ===== Is some important material missing from the book? In particular, this text has not yet been harmonized with the needs of [[chaosbook:discrete|Chapter "World in a mirror"]] and yet mostly unwritten (but essential) [[chaosbook:continuous|Chapter "Continuous symmetries"]]. ===== Section: Cycle Floquet multipliers are metric invariants ===== cycle stabilities are indeed metric invariants of flows ===== Rėsumė ===== Mark here when summary completed. ===== Commentary ===== Here all references to external literature (avoid them in the text proper, it is meant to be self-contained). ===== Exercises ===== ===== References ===== Mark here when correctly ordered. OK to have references not cited, as long as they are relevant to this chapter. ~~DISCUSSION~~
