Almost every great classical mechanics book has a huge chunk devoted to rigid body dynamics. For example, I'm going through Goldstein right now, and I'm anxious to get to Hamiltonian formalism and canonical transformations, but there's 100+ pages of rigid body dynamics in the way; I'm looking for motivation to study this topic, and maybe others are too.

  • What are the applications/analogies of rigid body dynamics to more modern areas of physics?
  • Why should the serious physics student be motivated to study rigid body dynamics beyond the surface level of simply understanding angular momentum and torque?
  • How does the study of rigid bodies help one better understand the Lagrangian/Hamiltonian formalisms?
  • Why is the rigid bodies section usually before the Hamiltonian section in CM books?
  • Basically, why should we care about rigid bodies if our interest is in modern physics (statistical mechanics, quantum mechanics, condensed matter, etc.)?
  • $\begingroup$ My opinion is that if you are self-studying you could skip over it. I don’t see much usefulness in other areas. I’m curious what others will tell you. $\endgroup$ – G. Smith Jan 29 at 0:44
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    $\begingroup$ "What are the applications/analogies of rigid body dynamics to more modern areas of physics?" Literally anything that's a rigid body. For example, the LHC, the space station, and most pieces of condensed matter are approximately rigid bodies, and so on. $\endgroup$ – knzhou Jan 29 at 0:45
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    $\begingroup$ You are of course free to skip over anything in a textbook that's not relevant for the advanced topics you're aiming at, but consider that these textbooks are already created by culling down 99.9% of work ever done. A classical mechanics book is like a list of the 'top 10 hits of physics in the 18th to 19th century' and it would be a shame to just skip half of them! You run the risk of building an incredibly top-heavy understanding that cannot be used to explain anything except for a few carefully controlled systems. $\endgroup$ – knzhou Jan 29 at 0:47
  • $\begingroup$ Nuclear rotational motion, molecular dynamics. It’s not a natural symplectic system since it has odd dimension and one constraint. Of course the dynamics in rotating frame (Coriolis effects etc) is essential to atmosphere modelling etc etc etc $\endgroup$ – ZeroTheHero Jan 29 at 0:53
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    $\begingroup$ Also, for most students, rigid bodies are also typically the first time you see a nontrivial configuration space, the first time you see tensors, the first time you see a Lie group/algebra, the first time physics shows you tremendously unintuitive but correct results, the first time you need to work in different "pictures" (space/body frames, like Heisenberg/Schrodinger picture in QM), and so on. It's a very rich example. $\endgroup$ – knzhou Jan 29 at 0:57

This question might be closed because of the multiple questions inside, so I am expanding on my comment:

There are multiple purposes for teaching physics at school. Most of them are for students who end up in engineering or other disciplines using physics in a background way. The courses are designed by physicists for future physists who may be doing applied physics or physics research for furthering the knowledge base of humanity.

We live and move in a classical mechanics world, which is well approximated by rigid bodies dynamics. In a sense we have an intuitive expectation even in our motion that depends on rigid body dynamics. For physicists and future physicists, the elaboration in the historical growth of mechanics can connect intuitions to strict mathematics.

One can acquire a subconscious background in mathematical physics tools that are useful when studying "statistical mechanics, quantum mechanics, condensed matter, etc".

For people going on to research, enriching the mathematical tools available , acquiring a mathematical intuition, is very useful.

Even for understanding the current research ways. Think how useful intuitve knowledge of strings is for helping an understanding of string theory.

This mathematical intuition was built and transferred by physicists after the revolution of using calculus in physics models, and the progress in understanding since then can be traced step by step. There would be no Maxwell equations if there had not been Newtonian mechanics.


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