Studying Analytical Mechanics this July

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Discussion Overview

The discussion centers around the choice of textbooks for studying analytical mechanics, specifically comparing Thornton and Marion's "Classical Dynamics of Particles and Systems" with Robert Fitzpatrick's "Newtonian Dynamics." Participants explore the implications of their choices on understanding key concepts such as Hamiltonian and Lagrangian mechanics.

Discussion Character

  • Exploratory
  • Debate/contested
  • Homework-related

Main Points Raised

  • One participant expresses a desire to learn analytical mechanics quickly but acknowledges the challenges of rushing through the material.
  • Another participant emphasizes the importance of spending adequate time on Hamiltonian and Lagrangian mechanics, sharing their experience of re-taking classical mechanics to gain a deeper understanding.
  • There is a concern about Fitzpatrick's book providing limited coverage of Hamiltonian and Lagrangian dynamics compared to Thornton and Marion's text.
  • Some participants suggest that Fitzpatrick's book may be a quicker option but question whether the title "Newtonian Dynamics" aligns with the broader scope of analytical mechanics.
  • A participant speculates on the distinction of "Analytical" in analytical mechanics, pondering if it differentiates from computational or numerical approaches.

Areas of Agreement / Disagreement

Participants do not reach a consensus on which textbook is preferable, with some advocating for Fitzpatrick's shorter text while others highlight the importance of comprehensive coverage in Thornton and Marion's book. The discussion remains unresolved regarding the implications of the titles and the depth of content in each book.

Contextual Notes

Participants express varying levels of familiarity with the textbooks and their content, indicating that assumptions about the coverage of topics like Hamiltonian and Lagrangian mechanics may depend on individual interpretations of the texts.

davidbenari
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So I'm taking analytical mechanics next semester. The textbook they use is Thornton and Marion's "Classical Dynamics of Particles and Systems".

I want to learn it all this month. It is feasible, but extenuating. But there is another option.

I could read Robert Fitzpatrick's Newtonian Dynamics http://farside.ph.utexas.edu/teaching/336k/Newton/index.html which is shorter, and probably contains the same topics. This book is recommended by Gerard t'Hooft's page on "How to become a good theoretical physicist".

Which one should I choose considering my hasty plans?

One drawback I consider from Fitzpatrick's book is that it contains only a small section on Hamiltonian and Lagrangian mechanics and it appears only till the end, while on Thornton and Marion, you are presented with it in the first 1/5 of the book, and I guess uses it till the end.

Suggestions?

Thanks.
 
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Some things cannot be rushed. I believe the more time you spend with Hamiltonian mechanics, the better physicist you will be.

Lagrangian too.

I ended up re-taking undergrad classical mechanics my first year of grad school (MIT), and I was better off because of it.

Take your time. As they say, if you don't have time to do it right, you must have time to do it again.
 
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I'll probably do it twice since I'll do it this month and during the next semester. But I do want to see all the topics involved in that class. I don't want to just see 20% of it. I have until about the 23rd of August to study.

Do you know anything about Fitzpatrick?
 
Graw said:
Humanity exctincted and after XXX years Earth is populated by "new" humans. How long could it take if exctinction happened in 2130?

davidbenari said:
I'll probably do it twice since I'll do it this month and during the next semester. But I do want to see all the topics involved in that class. I don't want to just see 20% of it. I have until about the 23rd of August to study.

Do you know anything about Fitzpatrick?

Looks solid, but as you mentioned Hamiltonian and Lagrangian dynamics get short shrift.

I prefer mechanics courses to include the Hamiltonian and Lagrangian approaches to a lot of problems all through the semester.
 
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I think i'll go for Fitzpatrick book, since it'll be a quicker ride. I had a question though: do you think the title "Newtonian Dynamics" conflicts with a book on Analytical Mechanics? My guess is that no, and by Newtonian Dynamics one simply refers to dynamics that relies on Newtons 3 laws, even if some of the mathematical formalisms weren't known to Newton (This is my guess).

Do you know why Analytical Mechanics is called Analytical? Is it meant to distinguish it from something having to do with "Computational" or "Numerical" physics?
 
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