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<- [[:chaosbook]]

====== Chapter: Hamiltonian dynamics ======

(ChaosBook.org blog, chapter [[http://chaosbook.org/paper.shtml#newton|Hamiltonian dynamics]])  --- //[[predrag.cvitanovic@physics.gatech.edu|Predrag Cvitanovic]] 2009-03-0//

{{:gtspring2009:gt.png|}}  I am bit puzzled by the introduction. The chapter is called Newtonian dynamics, but then goes straight to Hamiltonian flows (time-independent only). Even in the time-independent case, if one allows non-conservative forces in Newton's equation, energy is not conserved. We either need to specify this in the introduction, or we may want to call the chapter 'Hamiltonian Dynamics'.
 --- //[[gregor.tanner@nottingham.ac.uk|Gregor Tanner]]  2007-10-19//


===== Section: Hamiltonian flows =====

===== Section: Stability of Hamiltonian flows =====

==== Subsection: Canonical transformations ====

==== Subsection: Stability of equilibria of Hamiltonian flows ====

===== Section: Symplectic maps =====

==== Example: Standard map ====

===== (?) Section: Collinear helium =====

{{gtspring2009:pc.jpg}} If you want to move [[:chaosbook:conjug#sectioncollinear_helium|6.3 "Collinear helium"]]  to here, it is OK with me. I would place it ahead of Section "Poincaré invariants," which is of narrower interest. Originally it was here, but it did not make sense without defining smooth coordinate transformations first. If you harmonize it with this chapter, might work well.  --- //[[predrag.cvitanovic@physics.gatech.edu|Predrag Cvitanovic]] 2009-03-29//

{{:gtspring2009:gt.png|}} This section to be moved here from [[chaosbook:conjug|chapter "Get straight"]]. While I see the idea behind trying to match KS regularization with smooth conjugacy, I am not sure it works well. Collinear helium is singular (and you want smooth flows to start with), the transformation involves time (which is a new concept at that point), and one of the main points of the KS transformation is that the combination of time and space transformation keeps everything Hamiltonian (a point which comes too early here). In addition, this text was written with the helium quantization chapter, so it needs to be rewritten further. --- //[[gregor.tanner@nottingham.ac.uk|Gregor Tanner]]  2009-3-26//

{{gtspring2009:pc.jpg}} regularize the 2-body Coulomb collisions in classical helium.


===== Section: Poincaré invariants =====

===== Section: Reversibility =====

===== 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~~
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