Advanced Mechanics Book: Diff Geom Approach

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SUMMARY

The discussion centers on the search for advanced classical mechanics books that utilize differential geometry, specifically symplectic geometry, akin to Goldstein's work. Participants recommend several resources, including "An Introduction to Mechanics" by Daniel Kleppner and Robert Kolenkow, and "Classical Mechanics" by Herbert Goldstein, which are suitable for readers with varying levels of familiarity with differential geometry. The links provided lead to essential texts that facilitate the analysis of mechanics through a differential geometry lens.

PREREQUISITES
  • Understanding of classical mechanics principles.
  • Familiarity with differential geometry concepts.
  • Basic knowledge of symplectic geometry.
  • Experience with mathematical analysis techniques.
NEXT STEPS
  • Explore "An Introduction to Mechanics" by Daniel Kleppner and Robert Kolenkow.
  • Study "Classical Mechanics" by Herbert Goldstein for advanced concepts.
  • Research symplectic geometry applications in mechanics.
  • Review online resources and lecture notes on differential geometry in physics.
USEFUL FOR

Students, physicists, and researchers interested in advanced classical mechanics and its applications through differential geometry, particularly those looking to deepen their understanding of symplectic geometry.

NeroKid
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hello guys, I am wondering whether there's any book on classical mechanics on the level of Goldstein but using differential geometry language, no need for introducing to the differential geometry subject but mostly on how to analyse mechanics using it, tks
 
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Hi Nero! There are a wealth of books on that at different levels depending on how much differential geometry, particularly symplectic geometry, you already know. Some examples of introductory texts/notes:
https://www.amazon.com/dp/0387968903/?tag=pfamazon01-20
https://www.amazon.com/dp/0817641459/?tag=pfamazon01-20
http://math.ucr.edu/home/baez/classical/
https://www.amazon.com/dp/0521636361/?tag=pfamazon01-20
https://www.amazon.com/dp/0387406158/?tag=pfamazon01-20
https://www.amazon.com/dp/038798643X/?tag=pfamazon01-20
 
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tks for your recommendation
 

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