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Chapter: Hamiltonian dynamics

( blog, chapter Hamiltonian dynamics) — Predrag Cvitanovic 2009-03-0

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

If you want to move 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 2009-03-29

This section to be moved here from 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 buy dissertation, so it needs to be rewritten further. — Gregor Tanner 2009-3-26

regularize the 2-body Coulomb collisions in classical helium.

Section: Poincaré invariants

Section: Reversibility


Mark here when summary completed.


Here all references to external literature (avoid them in the text proper, it is meant to be self-contained).



chaosbook/newton.txt · Last modified: 2014/12/03 09:12 by predrag