Sources on explicitly time-dependent Hamiltonian formalism

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Discussion Overview

The discussion revolves around finding suitable sources for a thorough treatment of Hamiltonian formalism specifically in the context of explicitly time-dependent systems. The inquiry seeks recommendations for literature that adequately covers this topic, which may include theoretical and applied aspects.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant requests recommendations for sources on Hamiltonian formalism in explicitly time-dependent cases.
  • Another participant suggests a book on geometric formulation in classical and quantum mechanics, noting the difficulty in finding simple texts on the topic and recommending searches for "non-autonomous mechanics" or "non-autonomous dynamical systems."
  • A participant expresses concern that the suggested book may be too advanced, mentioning a preference for more straightforward texts and inquiring about Herbert Goldstein's book as a potential classic reference.
  • A later reply indicates a lack of responses to the initial inquiry, suggesting limited engagement or available resources on the topic.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on specific sources or the appropriateness of suggested literature, indicating that multiple views and uncertainties remain regarding suitable references for the topic.

Contextual Notes

Limitations include the potential complexity of recommended texts, the specificity of the topic, and the varying levels of familiarity with Hamiltonian formalism among participants.

Who May Find This Useful

Readers interested in advanced mechanics, particularly those focusing on Hamiltonian formalism and its applications in time-dependent systems, may find this discussion relevant.

TheoryofChaos
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Not sure I am posting this in the right subforum, if this is not the case, please feel free to move it.

Anyway, the title about sums it up - I need to find a good source which offers a thourough treatment of Hamiltonian formalism for the explicitly time-dependent case - could someone possibly suggest some?

Thanks in advance.
 
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I haven't personally read this book, but it looks like it could be useful:

https://www.amazon.com/Geometric-Formulation-Classical-Quantum-Mechanics/dp/9814313726/ref=sr_1_3?s=books&ie=UTF8&qid=1339477934&sr=1-3&keywords=non+autonomous+mechanics

I found it surprisingly difficult to locate simple texts covering this topic! It might help to search for the phrases non-autonomous mechanics or non-autonomous dynamical systems as well. There's also a big literature on ODEs under the name control theory which might be relevant.
 
Thanks for the post - This book, however, has "fiber bundles over R" as 1.1, not somewhat of a higher reach, then?

Also, theory of optimal control is, I think, supposed to be an extension of Hamiltonian formalism, I think I would be happy with a "non-extended" book for the time being.

Since Herbert Goldstein's book is considered to be a classic one in the field, and I haven't had a look at it, would anyone know if it treats the topics in any detail?

Thanks again.
 
Noone, then?
 

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