Quantcast
  • Register
PhysicsOverflow is a next-generation academic platform for physicists and astronomers, including a community peer review system and a postgraduate-level discussion forum analogous to MathOverflow.

Welcome to PhysicsOverflow! PhysicsOverflow is an open platform for community peer review and graduate-level Physics discussion.

Please help promote PhysicsOverflow ads elsewhere if you like it.

News

PO is now at the Physics Department of Bielefeld University!

New printer friendly PO pages!

Migration to Bielefeld University was successful!

Please vote for this year's PhysicsOverflow ads!

Please do help out in categorising submissions. Submit a paper to PhysicsOverflow!

... see more

Tools for paper authors

Submit paper
Claim Paper Authorship

Tools for SE users

Search User
Reclaim SE Account
Request Account Merger
Nativise imported posts
Claim post (deleted users)
Import SE post

Users whose questions have been imported from Physics Stack Exchange, Theoretical Physics Stack Exchange, or any other Stack Exchange site are kindly requested to reclaim their account and not to register as a new user.

Public \(\beta\) tools

Report a bug with a feature
Request a new functionality
404 page design
Send feedback

Attributions

(propose a free ad)

Site Statistics

205 submissions , 163 unreviewed
5,047 questions , 2,200 unanswered
5,345 answers , 22,709 comments
1,470 users with positive rep
816 active unimported users
More ...

  Reference Request: Classical Mechanics with Symplectic Reduction

+ 6 like - 0 dislike
951 views

I am trying to find a supplement to appendix of Cushman & Bates' book on Global aspects of Classical Integrable Systems, that is less terse and explains mechanics with Lie groups (with dual of Lie algebra) to prove Symplectic reduction theorem (on locally free proper G-action), Arnold-Liouville Theorem (on completely integrable systems) and some more.

For instance, both Arnold's mechanics book and Spivak's physics for mathematician does not explain these concepts. I think supplements will help me understand that book's appendix (where it explains reduction theorem with lots of machinery, Ehresmann connection, and so on). Any suggestions on this?

This post imported from StackExchange Physics at 2014-08-11 14:58 (UCT), posted by SE-user chhan92
asked Mar 26, 2013 in Theoretical Physics by chhan92 (30 points) [ no revision ]
retagged Aug 11, 2014
I think you should go for the canonical reference Foundations of mechanics by Abraham and Marsden. It has pretty much everything that you are talking about.

This post imported from StackExchange Physics at 2014-08-11 14:58 (UCT), posted by SE-user Sandeep Thilakan
Related: physics.stackexchange.com/q/26912/2451

This post imported from StackExchange Physics at 2014-08-11 14:58 (UCT), posted by SE-user Qmechanic
Arnold-Liouville theorem is in Arnold's book.

This post imported from StackExchange Physics at 2014-08-11 14:58 (UCT), posted by SE-user MBN

1 Answer

+ 0 like - 0 dislike

As for the symplectic reduction, a good place to look at is Chapter 6 of Olver's Applications of Lie Groups to Differential Equations. This chapter is almost independent from the rest of the book.

This post imported from StackExchange Physics at 2014-08-11 14:58 (UCT), posted by SE-user just-learning
answered Feb 21, 2014 by just-learning (95 points) [ no revision ]

Your answer

Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead.
To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL.
Please consult the FAQ for as to how to format your post.
This is the answer box; if you want to write a comment instead, please use the 'add comment' button.
Live preview (may slow down editor)   Preview
Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:
p$\varnothing$ysicsOverflow
Then drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds).
Please complete the anti-spam verification




user contributions licensed under cc by-sa 3.0 with attribution required

Your rights
...